Question

time to complete the square!
solve by completing the square.
$x^2 - 6x - 16 = 0$
note: if you have a square root that does not equal a whole number, round to the nearest tenth (1 decimal place). write your answer as #, # (for example, 1, -2).

Explanation:

Step1: Isolate constant term

$x^2 - 6x = 16$

Step2: Complete the square

Take half of -6: $\frac{-6}{2}=-3$, square it: $(-3)^2=9$. Add to both sides:
$x^2 - 6x + 9 = 16 + 9$
$(x - 3)^2 = 25$

Step3: Take square root of both sides

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

Step4: Solve for x

Case 1: $x - 3 = 5$
$x = 5 + 3 = 8$
Case 2: $x - 3 = -5$
$x = -5 + 3 = -2$

Answer:

8, -2