Question

Find the roots of the equation $x^2–18x+12=0$ by the method of completing the square.

• A. $x=9\pm \sqrt{69}$
• B. $x=9\pm \sqrt{67}$
• C. $x=6\pm \sqrt{69}$
• D. $x=8\pm \sqrt{69}$

Answer 1

The correct option is A $x=9\pm \sqrt{69}$

Given: $x^2–18x+12=0$
This is same as:
$x^2–[2\times (x)\times 9]+9^2–9^2+12=0$
$\Rightarrow (x–9{)}^2–81+12=0$
$\Rightarrow (x–9{)}^2–69=0$
$\Rightarrow (x–9{)}^2=69$
$\Rightarrow x-9=\pm \sqrt{69}$
$\Rightarrow x=9\pm \sqrt{69}$