Question

Solve the quadratic equation $2x^2+x-4=0$ by completing the square

Answer 1

The given quadratic equation is

$2x^2+x-4=0$

$\Rightarrow x^2+\frac{x}{2}-2=0$

$\Rightarrow x^2+\frac{x}{2}=2$

On adding both sides $\frac{1}{16}$ we get

$x^2+\frac{x}{2}+\frac{1}{16}=2+\frac{1}{16}$

$\Rightarrow {(x+\frac{1}{4})}^2=\frac{33}{16}$

$\Rightarrow x+\frac{1}{4}=\pm \frac{\sqrt{33}}{4}$

$\Rightarrow x=\pm \frac{\sqrt{33}}{4}-\frac{1}{4}$

$\Rightarrow x=\frac{-1-\sqrt{33}}{4},\frac{-1+\sqrt{33}}{4}$