Question

Solve the following quadratic equation by completing square method
$x^2+11x+24=0$

Answer 1

Given equation:

$x^2+11x+24=0$

Adding ${\left(\frac{11}{2}\right)}^2$ on both side, we get

$x^2+11x+\frac{121}{4}+24=\frac{121}{4}$

$\Rightarrow {(x+\frac{11}{2})}^2=\frac{121}{4}-24=\frac{25}{4}$

$\Rightarrow x+\frac{11}{2}=\pm \frac{5}{2}$

$\Rightarrow x=\pm \frac{5}{2}-\frac{11}{2}$

$\Rightarrow x=-8$ or $x=-3$