Question

Find the roots of the following quadratic equation, by the method of completing the square:
$2x^2+x-4=0$

Answer 1

$2x^2+x-4=0$
$\Rightarrow 2x^2+x=4$
On dividing both sides of the equation by 2, we get;
$\Rightarrow x^2+\frac{x}{2}=2$
On adding $(\frac{1}{4}{)}^2$ to both sides of the equation, we get
$\Rightarrow (x{)}^2+2\times x\times \frac{1}{4}+(\frac{1}{4}{)}^2=2+(\frac{1}{4}{)}^2\Rightarrow (x+\frac{1}{4}{)}^2=\frac{33}{16}\Rightarrow x+\frac{1}{4}=\pm \frac{\sqrt{33}}{4}$
$\Rightarrow x$ = $\pm \frac{\sqrt{33}}{4}-\frac{1}{4}$
$\Rightarrow x$ = $\pm \frac{\sqrt{33}-1}{4}$
$\Rightarrow x$= $\frac{\sqrt{33}-1}{4}$ or $x=\frac{-\sqrt{33}-1}{4}$