Solve the equation by completing the square: m^2+12m+19=0

Question

A. 10.12, -1.88
B. -10.12, -1.88
C. 10.12, 1.88
D. -10.12, 1.88

Answer 1

First, we need to complete the square for the given equation m^2 + 12m + 19 = 0.

m^2 + 12m + 19 = 0
(m + 6)^2 - 36 + 19 = 0
(m + 6)^2 - 17 = 0
(m + 6)^2 = 17

Now, take the square root of both sides:

m + 6 = ±√17
m = -6 ± √17

Therefore, the solutions are:
m = -6 + √17 ≈ -1.88
m = -6 - √17 ≈ -10.12

Therefore, the correct answer is B. -10.12, -1.88