Question

solve by completing the square
$x^2 - 2x - 12 = 0$
select the correct response:
$x = 16$
$x = -15$
$x = 14$
$x = -12$
$x = 1 + \sqrt{13}$
$x = 1 - \sqrt{13}$
$x = 1 + \sqrt{15}$
$x = 1 - \sqrt{15}$

Explanation:

Step1: Move constant to right

Given \(x^2 - 2x - 12 = 0\), add 12 to both sides:
\(x^2 - 2x = 12\)

Step2: Complete the square

Take half of \(-2\) (which is \(-1\)), square it (\((-1)^2 = 1\)), add to both sides:
\(x^2 - 2x + 1 = 12 + 1\)
This factors to \((x - 1)^2 = 13\)

Step3: Solve for \(x\)

Take square roots: \(x - 1 = \pm\sqrt{13}\)
Add 1 to both sides: \(x = 1 \pm\sqrt{13}\)

Answer:

\(x = 1 + \sqrt{13}\), \(x = 1 - \sqrt{13}\)