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