Question

Solve the quadratic equation $5x^2+10x-2=0$ by completing the square method.

Answer 1

$5x^2+10x-2=0$
$\Rightarrow 5x^2+10x=2$
On dividing both sides of the equation by 2, we get,
$\Rightarrow x^2+\frac{10x}{5}=\frac{2}{5}$
$\Rightarrow x^2+2\times x\times 1=\frac{2}{5}$
On adding $1^2$ to both sides of equation, we get
$\Rightarrow (x{)}^2+2\times x\times 1+(1{)}^2=(1{)}^2+\frac{2}{5}$

$\Rightarrow (x+1{)}^2=\frac{7}{5}$

$\Rightarrow (x+1)=\pm \sqrt{\frac{7}{5}}$
$\Rightarrow x=-1\pm \sqrt{\frac{7}{5}}$