Question
Solve the following quadratic equation by completing the square method.
x2 + 2x – 5 = 0
x2 + 2x – 5 = 0
✓
Answer
$\begin{array}{l}x^2+2 x-5=0 \\ \Rightarrow x^2+2 x+1-1-5=0 \\ \Rightarrow\left(x^2+2 x+1\right)-(1+5)=0 \\ \Rightarrow(x+1)^2-6=0 \\ \Rightarrow(x+1)^2=6 \\ \Rightarrow x+1=\sqrt{6} \\ \Rightarrow x+1= \pm \sqrt{6} \\ \Rightarrow x+1=\sqrt{6} \text { or } x+1=-\sqrt{6}\end{array}$
$\Rightarrow x=\sqrt{6}-1$ or $x=-\sqrt{6}-1$
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