Question
Solve the following quadratic equation by completing the square method.
$x^2+x-20=0$

Answer

$x^2+x-20=0 $
$\Rightarrow x ^2+ x +\frac{1}{4}-\frac{1}{4}-20=0 $
$\Rightarrow\left(x^2+x+\frac{1}{4}\right)+\left(\frac{1}{4}-20\right)=0 $
$\Rightarrow\left( x +\frac{1}{2}\right)^2-\frac{1+80}{4}=0 $
$\Rightarrow\left(x+\frac{1}{2}\right)^2=\frac{81}{4} $
$\Rightarrow x +\frac{1}{2}=\sqrt{\frac{81}{4}} $
$\Rightarrow x+\frac{1}{2}= \pm \frac{9}{2} $
$\Rightarrow x +\frac{1}{2}=\frac{9}{2} \text { or } x +\frac{1}{2}=-\frac{9}{2} $
$\Rightarrow x =\frac{9}{2}-\frac{1}{2} \text { or } x =-\frac{9}{2}-\frac{1}{2} $
$\Rightarrow x =\frac{8}{2} \text { or } x =-\frac{10}{2} $
$\Rightarrow x=4 \text { or } x=-5$

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