Question

Solve the following quadratic equation for $x$ by completing the square method: $x^2-4x-11=0$

Answer 1

$x^2-4x-11=0$
$⟹x^2-4x+4-4-11=0$
$⟹x^2-4x+4-15=0$
$⟹x^2-(2\times 2\times x)+(2{)}^2-15=0$
$⟹(x-2{)}^2-(\sqrt{15}{)}^2=0$
$⟹(x-2+\sqrt{15})$$\times (x-2-\sqrt{15})=0$
$⟹(x-2+\sqrt{15})=0$ or $(x-2-\sqrt{15})=0$
$⟹x=2-\sqrt{15}$ or $x=2+\sqrt{15}$

$\therefore 2-\sqrt{15}$ and $2+\sqrt{15}$ are the roots of the given quadratic equation.