Question

what are the values of x in the equation $x^2 - 6x + 9 = 25$?
$\bigcirc$ $x = -2$ or $x = 8$
$\bigcirc$ $x = -1$ or $x = -11$
$\bigcirc$ $x = 1$ or $x = 11$
$\bigcirc$ $x = 2$ or $x = -8$

Explanation:

Step1: Rewrite left side as square

$x^2 - 6x + 9 = (x-3)^2$, so equation becomes $(x-3)^2 = 25$

Step2: Take square roots both sides

$x-3 = \pm\sqrt{25} = \pm5$

Step3: Solve for x (case 1)

$x-3 = 5 \implies x = 5 + 3 = 8$

Step4: Solve for x (case 2)

$x-3 = -5 \implies x = -5 + 3 = -2$

Answer:

A. $x = -2$ or $x = 8$