Question

solve the quadratic equation by completing the square.
$x^2 - 10x - 8 = 0$
the solution set is .
(type an exact answer, using radicals as needed. use a comma to separate answers as needed.)

Explanation:

Step1: Isolate constant term

$x^2 - 10x = 8$

Step2: Complete the square

Take half of $-10$: $\frac{-10}{2}=-5$, square it: $(-5)^2=25$. Add to both sides:
$x^2 - 10x + 25 = 8 + 25$
$(x - 5)^2 = 33$

Step3: Solve for x

Take square root of both sides:
$x - 5 = \pm\sqrt{33}$

Step4: Isolate x

$x = 5 \pm\sqrt{33}$

Answer:

$5+\sqrt{33}, 5-\sqrt{33}$