Question

solve by complating the square,
$x^2 + 10x - 24 = 0$
select the correct response:
$x = \sqrt{24}$
$x = -\sqrt{24}$
$x = -2$
$x = 12$
$x = \sqrt{124}$
$x = -\sqrt{124}$
$x = 2$
$x = -12$

Explanation:

Step1: Move constant to right

$x^2 + 10x = 24$

Step2: Complete the square

Take half of 10, square it: $(\frac{10}{2})^2 = 25$. Add to both sides:
$x^2 + 10x + 25 = 24 + 25$
$(x + 5)^2 = 49$

Step3: Take square root

$x + 5 = \pm\sqrt{49} = \pm7$

Step4: Solve for x

Case 1: $x + 5 = 7 \implies x = 2$
Case 2: $x + 5 = -7 \implies x = -12$

Answer:

$x = 2$
$x = -12$