Question

Find the roots of the equation $x^2–4x-9=0$ by the method of completing the square.

• A. $x=4\pm \sqrt{-5}$
• B. $x=2\pm \sqrt{-3}$
• C. $x=2\pm \sqrt{-6}$
• D. $x=2\pm \sqrt{-5}$

Answer 1

The correct option is D $x=2\pm \sqrt{-5}$

Given: $x^2–4x-9=0$
This is same as:
$x^2–[2\times (x)\times 2]+2^2–2^2-9=0$
$\Rightarrow (x–2{)}^2–4-9=0$
$\Rightarrow (x–2{)}^2-13=0$
$\Rightarrow (x–2{)}^2=13$
$\Rightarrow x-2=\pm \sqrt{13}$
$\Rightarrow x=2\pm \sqrt{13}$