Solve each equation by completing the square

r² = - 12r - 35

r = - 7, r = - 5

Step-by-step explanation:

Given

r² = - 12r - 35 (add 12r to both sides)

r² + 12r = - 35

To complete the square

add (half the coefficient of the r - term) ² to both sides

r² + 2 (6) r + 36 = - 35 + 36

(r + 6) ² = 1 ← take the square root of both sides)

r + 6 = ± 1 (subtract 6 from both sides)

r = - 6 ± 1, thus

r = - 6 - 1 = - 7 or r = - 6 + 1 = - 5