Question

Find the roots of equation $2x^2-x-4=0$ by the method of completing the square.

Answer 1

Method of completing the square,

Given equation is $2x^2-x-4=0$

The coefficient of $x^2$ is $2$, make it $1$ by dividing by $2$ on both the sides.

i.e. $x^2-\frac{x}{2}-2=0$

Transpose the constant term to the right.

$x^2-\frac{x}{2}=2$

Add the square of half the coefficient of $x$ on both sides.

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

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

The equation is of the form

$a^2=b$

which implies

$a=\pm \sqrt{b}$

Therefore,

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

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