怎么求X

无论你是求指数还是自由基，或者只是做一些乘除，都有许多方法可以求解x。不管你使用那种方法，你总是得找到一种方法将x独立到方程的一侧，从而找到它的值。接下来将教你怎么做：

方法 1 的 5:

使用基本的线性方程

  1. {"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/2\/2f\/Solve-for-X-Step-1-Version-4.jpg\/v4-460px-Solve-for-X-Step-1-Version-4.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/2\/2f\/Solve-for-X-Step-1-Version-4.jpg\/v4-728px-Solve-for-X-Step-1-Version-4.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"} 1 写下题目。像这样：
    • 22(x+3) + 9 - 5 = 32
  2. {"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/9\/99\/Solve-for-X-Step-2-Version-4.jpg\/v4-460px-Solve-for-X-Step-2-Version-4.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/9\/99\/Solve-for-X-Step-2-Version-4.jpg\/v4-728px-Solve-for-X-Step-2-Version-4.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"} 2 求指数。记住操作的顺序：PEMDAS，代表括号，指数，乘法/除法，加法/减法。你不能首先解括号因为x是括号中的，所以你应该从指数开始，即22。 22 = 4
    • 4(x+3) + 9 - 5 = 32
  3. {"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/e\/ea\/Solve-for-X-Step-3-Version-4.jpg\/v4-460px-Solve-for-X-Step-3-Version-4.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/e\/ea\/Solve-for-X-Step-3-Version-4.jpg\/v4-728px-Solve-for-X-Step-3-Version-4.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"} 3 做乘法。将4乘入(x +3)。像这样：
    • 4x + 12 + 9 - 5 = 32
  4. {"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/6\/60\/Solve-for-X-Step-4-Version-4.jpg\/v4-460px-Solve-for-X-Step-4-Version-4.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/6\/60\/Solve-for-X-Step-4-Version-4.jpg\/v4-728px-Solve-for-X-Step-4-Version-4.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"} 4 做加减法。将剩下的数加上或减去。像这样：
    • 4x+21-5 = 32
    • 4x+16 = 32
    • 4x + 16 - 16 = 32 - 16
    • 4x = 16
  5. {"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/a\/a1\/Solve-for-X-Step-5-Version-4.jpg\/v4-460px-Solve-for-X-Step-5-Version-4.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/a\/a1\/Solve-for-X-Step-5-Version-4.jpg\/v4-728px-Solve-for-X-Step-5-Version-4.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"} 5 分离变量。为此，只需将等式两边同时除以4以求得 x。4x/4 = x及16/4 = 4，因此x = 4。
    • 4x/4 = 16/4
    • x = 4
  6. {"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/5\/5e\/Solve-for-X-Step-6-Version-4.jpg\/v4-460px-Solve-for-X-Step-6-Version-4.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/5\/5e\/Solve-for-X-Step-6-Version-4.jpg\/v4-728px-Solve-for-X-Step-6-Version-4.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"} 6 检查你的计算。将x = 4带入原方程，确保原方程成立。像这样：
    • 22(x+3)+ 9 - 5 = 32
    • 22(4+3)+ 9 - 5 = 32
    • 22(7) + 9 - 5 = 32
    • 4(7) + 9 - 5 = 32
    • 28 + 9 - 5 = 32
    • 37 - 5 = 32
    • 32 = 32
方法 2 的 5:

含指数方程

  1. {"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/3\/32\/Solve-for-X-Step-7-Version-4.jpg\/v4-460px-Solve-for-X-Step-7-Version-4.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/3\/32\/Solve-for-X-Step-7-Version-4.jpg\/v4-728px-Solve-for-X-Step-7-Version-4.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"} 1 写下题目。假设你要解的题目里，x项包含指数：
    • 2x2 + 12 = 44
  2. {"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/4\/48\/Solve-for-X-Step-8-Version-4.jpg\/v4-460px-Solve-for-X-Step-8-Version-4.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/4\/48\/Solve-for-X-Step-8-Version-4.jpg\/v4-728px-Solve-for-X-Step-8-Version-4.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"} 2 分离指数项。首先你应该合并同类项，让所有的常数项都在方程右边，含指数项都在方程左边。等式两边同时减去12，像这样：
    • 2x2+12-12 = 44-12
    • 2x2 = 32
  3. {"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/3\/31\/Solve-for-X-Step-9-Version-4.jpg\/v4-460px-Solve-for-X-Step-9-Version-4.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/3\/31\/Solve-for-X-Step-9-Version-4.jpg\/v4-728px-Solve-for-X-Step-9-Version-4.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"} 3 将两边同时除以x项的系数以分离含指数的变量。在这种情况下，2是x的系数，因此将等式两边同时除以2以抵消。像这样：
    • (2x2)/2 = 32/2
    • x2 = 16
  4. {"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/f\/f2\/Solve-for-X-Step-10-Version-4.jpg\/v4-460px-Solve-for-X-Step-10-Version-4.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/f\/f2\/Solve-for-X-Step-10-Version-4.jpg\/v4-728px-Solve-for-X-Step-10-Version-4.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"} 4 将等式两边同时求得平方根。求出x2的平方根就能解出x。因此，将等式两边求出平方根，就能得x在等式的一边，以及16的平方根，4，在等式的另一边。因此x = 4。
  5. {"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/6\/63\/Solve-for-X-Step-11-Version-4.jpg\/v4-460px-Solve-for-X-Step-11-Version-4.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/6\/63\/Solve-for-X-Step-11-Version-4.jpg\/v4-728px-Solve-for-X-Step-11-Version-4.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"} 5 检查你的运算。将x = 4带入原方程中看结果是否满足。像这样：
    • 2x2 + 12 = 44
    • 2 x (4)2 + 12 = 44
    • 2 x 16 + 12 = 44
    • 32 + 12 = 44
    • 44 = 44
方法 3 的 5:

使用分数

  1. {"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/3\/3b\/Solve-for-X-Step-12-Version-4.jpg\/v4-460px-Solve-for-X-Step-12-Version-4.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/3\/3b\/Solve-for-X-Step-12-Version-4.jpg\/v4-728px-Solve-for-X-Step-12-Version-4.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"} 1 写下题目。假设你要解这样一个题目：[1]
    • (x + 3)/6 = 2/3
  2. {"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/a\/ab\/Solve-for-X-Step-13-Version-4.jpg\/v4-460px-Solve-for-X-Step-13-Version-4.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/a\/ab\/Solve-for-X-Step-13-Version-4.jpg\/v4-728px-Solve-for-X-Step-13-Version-4.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"} 2 交叉相乘。只需将每个分数的分母与其它分数的分子相乘。你只需在两条对角线上做乘法。因此，用第一个分数的分母6，乘以第二个分数的分子，2，在等式的右边得到12。将第二个分数的分母3，乘上第一个分数的分子x + 3，在等式的左边得到3 x + 9。过程展示如下：
    • (x + 3)/6 = 2/3
    • 6 x 2 = 12
    • (x + 3) x 3 = 3x + 9
    • 3x + 9 = 12
  3. {"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/6\/63\/Solve-for-X-Step-14-Version-4.jpg\/v4-460px-Solve-for-X-Step-14-Version-4.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/6\/63\/Solve-for-X-Step-14-Version-4.jpg\/v4-728px-Solve-for-X-Step-14-Version-4.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"} 3 合并同类项。将等式中的常数项合并，将等式两边同时减去9。过程展示如下：
    • 3x + 9 - 9 = 12 - 9
    • 3x = 3
  4. {"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/9\/92\/Solve-for-X-Step-15-Version-4.jpg\/v4-460px-Solve-for-X-Step-15-Version-4.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/9\/92\/Solve-for-X-Step-15-Version-4.jpg\/v4-728px-Solve-for-X-Step-15-Version-4.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"} 4 将每一项同时除以x以分离出x。只需将3x和9除以3, 即x的系数, 以求得x。3x/3 = x 及 3/3 = 1, 因此得出x = 1。
  5. {"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/f\/f0\/Solve-for-X-Step-16-Version-4.jpg\/v4-460px-Solve-for-X-Step-16-Version-4.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/f\/f0\/Solve-for-X-Step-16-Version-4.jpg\/v4-728px-Solve-for-X-Step-16-Version-4.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"} 5 检查你的运算。为了检查运算过程，只需将x带入原始方程中看方程是否成立。像这样：
    • (x + 3)/6 = 2/3
    • (1 + 3)/6 = 2/3
    • 4/6 = 2/3
    • 2/3 = 2/3
方法 4 的 5:

含根号的方程

  1. {"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/7\/7d\/Solve-for-X-Step-17-Version-3.jpg\/v4-460px-Solve-for-X-Step-17-Version-3.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/7\/7d\/Solve-for-X-Step-17-Version-3.jpg\/v4-728px-Solve-for-X-Step-17-Version-3.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"} 1 写下题目。假设你要解这样一个题目：[2]
    • √(2x+9) - 5 = 0
  2. {"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/3\/3e\/Solve-for-X-Step-18-Version-3.jpg\/v4-460px-Solve-for-X-Step-18-Version-3.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/3\/3e\/Solve-for-X-Step-18-Version-3.jpg\/v4-728px-Solve-for-X-Step-18-Version-3.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"} 2 分离平方根。在开始之前，你需要先将带平方根的项移到等式的同一边。因此，你要将等式两边同时加上5。像这样：
    • √(2x+9) - 5 + 5 = 0 + 5
    • √(2x+9) = 5
  3. {"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/f\/f2\/Solve-for-X-Step-19-Version-3.jpg\/v4-460px-Solve-for-X-Step-19-Version-3.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/f\/f2\/Solve-for-X-Step-19-Version-3.jpg\/v4-728px-Solve-for-X-Step-19-Version-3.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"} 3 将两边开根号。就像你将等式两边同时乘以x的系数一样，如果x在根号内，你需要将等式两边开根号。这样就能将根号从等式中去除了。像这样：
    • (√(2x+9))2 = 52
    • 2x + 9 = 25
  4. {"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/c\/c6\/Solve-for-X-Step-20-Version-3.jpg\/v4-460px-Solve-for-X-Step-20-Version-3.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/c\/c6\/Solve-for-X-Step-20-Version-3.jpg\/v4-728px-Solve-for-X-Step-20-Version-3.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"} 4 合并同类项。将等式两边同时减去9以合并同类项。所有常数项都在等式右边，x在等式左边。像这样：
    • 2x + 9 - 9 = 25 - 9
    • 2x = 16
  5. {"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/d\/d6\/Solve-for-X-Step-21-Version-3.jpg\/v4-460px-Solve-for-X-Step-21-Version-3.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/d\/d6\/Solve-for-X-Step-21-Version-3.jpg\/v4-728px-Solve-for-X-Step-21-Version-3.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"} 5 分离变量。最后一步求解x就是分离变量了。将等式两边同时除以2，x项的系数。2x/2 = x及16/2 = 8, 因此就得出了x = 8。
  6. {"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/a\/aa\/Solve-for-X-Step-22-Version-3.jpg\/v4-460px-Solve-for-X-Step-22-Version-3.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/a\/aa\/Solve-for-X-Step-22-Version-3.jpg\/v4-728px-Solve-for-X-Step-22-Version-3.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"} 6 检查你的运算。将8代入原方程的x处，检查你的结果是否正确：
    • √(2x+9) - 5 = 0
    • √(2(8)+9) - 5 = 0
    • √(16+9) - 5 = 0
    • √(25) - 5 = 0
    • 5 - 5 = 0
方法 5 方法 5 的 5:

含绝对值的方程

  1. {"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/5\/58\/Solve-for-X-Step-23-Version-3.jpg\/v4-460px-Solve-for-X-Step-23-Version-3.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/5\/58\/Solve-for-X-Step-23-Version-3.jpg\/v4-728px-Solve-for-X-Step-23-Version-3.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"} 1 写下题目。 假设你要解这样一个题目：[3]
    • |4x +2| - 6 = 8
  2. {"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/e\/e8\/Solve-for-X-Step-24-Version-3.jpg\/v4-460px-Solve-for-X-Step-24-Version-3.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/e\/e8\/Solve-for-X-Step-24-Version-3.jpg\/v4-728px-Solve-for-X-Step-24-Version-3.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"} 2 分离变量。首先你应该合并同类项，并将含绝对值的内容放在等式一边。在这道题中，可以将等式两边同时加上6，像这样：
    • |4x +2| - 6 = 8
    • |4x +2| - 6 + 6 = 8 + 6
    • |4x +2| = 14
  3. {"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/9\/9a\/Solve-for-X-Step-25-Version-3.jpg\/v4-460px-Solve-for-X-Step-25-Version-3.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/9\/9a\/Solve-for-X-Step-25-Version-3.jpg\/v4-728px-Solve-for-X-Step-25-Version-3.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"} 3 去除绝对值符号并解方程。这是第一步也是最简单的一部。不论什么情况下，你都应该求解两次x的值。第一次求解如下：
    • 4x + 2 = 14
    • 4x + 2 - 2 = 14 -2
    • 4x = 12
    • x = 3
  4. {"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/5\/57\/Solve-for-X-Step-26-Version-3.jpg\/v4-460px-Solve-for-X-Step-26-Version-3.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/5\/57\/Solve-for-X-Step-26-Version-3.jpg\/v4-728px-Solve-for-X-Step-26-Version-3.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"} 4 去除绝对值符号并改变等式另一边数值的符号。现在，再求解一次，除了将等式的另一部分定为-14而不是14。像这样：
    • 4x + 2 = -14
    • 4x + 2 - 2 = -14 - 2
    • 4x = -16
    • 4x/4 = -16/4
    • x = -4
  5. {"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/c\/c3\/Solve-for-X-Step-27-Version-3.jpg\/v4-460px-Solve-for-X-Step-27-Version-3.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/c\/c3\/Solve-for-X-Step-27-Version-3.jpg\/v4-728px-Solve-for-X-Step-27-Version-3.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"} 5 检查你的运算。现在你知道x = (3, -4)，只需将x带入原方程看它是否成立。像这样：
    • (对于 x = 3):
      • |4x +2| - 6 = 8
      • |4(3) +2| - 6 = 8
      • |12 +2| - 6 = 8
      • |14| - 6 = 8
      • 14 - 6 = 8
      • 8 = 8
    • (对于 x = -4):
      • |4x +2| - 6 = 8
      • |4(-4) +2| - 6 = 8
      • |-16 +2| - 6 = 8
      • |-14| - 6 = 8
      • 14 - 6 = 8
      • 8 = 8

小提示

  • 为了检验结果，将x的值带入原方程中并计算。
  • 自由基，即方根，是指数的另一种表现形式。x的平方根 = x^1/2。

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