Question

Solve the following quadratic equation by completing square method
$x^2+10x+24=0$

Answer 1

$x^2+10x+24=x$

$\therefore x^2+10=-24$ .......$\left(i\right)$

Third term $={\left(\frac{1}{2}\text{coefficient of}x\right)}^2$

$={(\frac{1}{2}\times 10)}^2$

$=25$

Adding 25 to both sides of equation (1), we get

$x^2+10x+25=-24+25$

$\therefore (x+5{)}^2=(1{)}^2$

Taking square roots on both sides

$x+5=\pm 1$

$x=-5\pm 1$

$x=-5+1=-4$

or $x=-5-1=-6$

Hence $-4$ and $-6$ are the roots of the given quadratic equation.