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
To solve the equation m^2 + 12m + 19 = 0 by completing the square, follow these steps:
1. Move the constant term to the other side of the equation:
m^2 + 12m = -19
2. To complete the square, take half of the coefficient of m (which is 12) and square it:
(12/2)^2 = 6^2 = 36
3. Add and subtract this value inside the parenthesis on the left side of the equation:
m^2 + 12m + 36 = -19 + 36
(m + 6)^2 = 17
4. Take the square root of both sides of the equation to solve for m:
m + 6 = ±√17
m = -6 ± √17
So the solutions to the equation m^2 + 12m + 19 = 0 are:
m = -6 + √17 ≈ -1.88
m = -6 - √17 ≈ -10.88
Therefore, the correct answer is:
b. -10.12, -1.88