Solve the equation by completing the square: m^2+ 12m + 19 = 0
a. 10.12, -1.88
b. -10.12, -1.88
c. 10.12, 1.88
d. -10.12, 1.88
First, move the constant to the other side of the equation:
m^2 + 12m = -19
Next, half the coefficient of m, square it, and add it to both sides of the equation to complete the square:
m^2 + 12m + 36 = -19 + 36
(m + 6)^2 = 17
Now take the square root of both sides:
m + 6 = ±√17
Now solve for m:
m = -6 ± √17
So the solutions are:
m = -6 + √17 or m = -6 - √17
This simplifies to approximately:
m ≈ 1.88 or m ≈ -10.88
The correct answer is c. 10.12, 1.88