Question

solve the equation.
$x^2 + 10x + 25 = 4$
$\circ$ $x = \\{-3, -7\\}$
$\circ$ $x = \\{-3, 3\\}$
$\circ$ $x = \\{7, -7\\}$
$\circ$ $x = \\{7, 3\\}$

Explanation:

Step1: Rewrite left side as square

$x^2 + 10x + 25 = (x+5)^2$
Equation becomes: $(x+5)^2 = 4$

Step2: Take square roots both sides

$x+5 = \pm\sqrt{4}$
$x+5 = \pm2$

Step3: Solve for x (case 1)

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

Step4: Solve for x (case 2)

$x+5 = -2$
$x = -2 - 5 = -7$

Answer:

$x = \{-3, -7\}$