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# 简单二次方程求解回顾

x^2=4 这样简单的二次方程可以通过取平方根来求解。本文回顾了几个例子，给你自己练习的机会。

$a{x}^{2}+bx+c=0$

### 例题1

$\begin{array}{rl}3{x}^{2}-7& =5\\ \\ 3{x}^{2}& =12\\ \\ {x}^{2}& =4\\ \\ \sqrt{{x}^{2}}& =±\sqrt{4}\\ \\ x& =±2\end{array}$

• $x=2$
• $x=-2$

$x=2$$x=-2$
$\begin{array}{rl}3{x}^{2}-7& =5\\ \\ 3\left(2{\right)}^{2}-7& =5\\ \\ 3\cdot 4-7& =5\\ \\ 12-7& =5\\ \\ 5& =5\end{array}$$\begin{array}{rl}3{x}^{2}-7& =5\\ \\ 3\left(-2{\right)}^{2}-7& =5\\ \\ 3\cdot 4-7& =5\\ \\ 12-7& =5\\ \\ 5& =5\end{array}$

### 例题 2

$\begin{array}{rl}\left(x-3{\right)}^{2}-81& =0\\ \\ \left(x-3{\right)}^{2}& =81\\ \\ \sqrt{\left(x-3{\right)}^{2}}& =±\sqrt{81}\\ \\ x-3& =±9\\ \\ x& =±9+3\end{array}$

• $x=+9+3=12$
• $x=-9+3=-6$

$x=12$$x=-6$
$\begin{array}{rl}\left(x-3{\right)}^{2}-81& =0\\ \\ \left(12-3{\right)}^{2}-81& =0\\ \\ {9}^{2}-81& =0\\ \\ 81-81& =0\\ \\ 0& =0\end{array}$$\begin{array}{rl}\left(x-3{\right)}^{2}-81& =0\\ \\ \left(-6-3{\right)}^{2}-81& =0\\ \\ \left(-9{\right)}^{2}-81& =0\\ \\ 81-81& =0\\ \\ 0& =0\end{array}$

$\left(x+1{\right)}^{2}-36=0$