Solve the following quadratic equation by completing the square m… - Vidyadip

Question

Solve the following quadratic equation by completing the square method.
x² + x – 20 = 0

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Answer

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

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