Solve the equation by completing the square: m^2+12m+19=0
To solve this equation by completing the square, follow these steps:
1. Move the constant to the other side of the equation:
m^2 + 12m = -19
2. Find the value that completes the square by taking half of the coefficient of m (which is 12) and squaring it:
12/2 = 6
6^2 = 36
3. Add and subtract this value inside the parentheses 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 to solve for m:
m + 6 = ±√17
m = -6 ± √17
Therefore, the solution to the equation by completing the square is:
m = -6 ± √17