Question

Find the roots of the equation $x^2–14x+17=0$ by the method of completing the square.

• A. $x=7\pm \sqrt{52}$
• B. $x=11\pm \sqrt{32}$
• C. $x=7\pm \sqrt{32}$
• D. $x=10\pm \sqrt{32}$

Answer 1

The correct option is C $x=7\pm \sqrt{32}$

Given : $x^2–14x+17=0$

This is same as:
$x^2–[2\times (x)\times 7]+7^2–7^2+17=0$
$\Rightarrow (x–7{)}^2–49+17=0$
$\Rightarrow (x–7{)}^2-32=0$
$\Rightarrow (x–7{)}^2=32$
$\Rightarrow x-7=\pm \sqrt{32}$
$\Rightarrow x=7\pm \sqrt{32}$