Solve by completing the square

Question

-4q^2-72q=100
write your answers and integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth

Answer 1

To solve this equation by completing the square, we first need to factor out the coefficient of q^2:

-4q^2 - 72q = 100
-q^2 - 18q = 25

Now, we complete the square by taking half of the coefficient of q (-18/2 = -9), squaring it (-9^2 = 81), and adding and subtracting it inside the parenthesis:

-(q^2 + 18q + 81) = 25 - 81
-(q + 9)^2 = -56
q + 9 = ±√56
q = -9 ± √56
q = -9 ± 2√14

Therefore, the solutions are:
q = -9 + 2√14
q = -9 - 2√14