Solve the equation by completing the square: m^2+ 12m + 19 = 0
To solve the equation by completing the square, we need to rewrite it in the form of (m + n)^2 = k.
First, move the constant term to the right side:
m^2 + 12m = -19
Next, find the value that will complete the square by taking half of the coefficient of m, squaring it, and adding it to both sides:
(12/2)^2 = 6^2 = 36
m^2 + 12m + 36 = -19 + 36
(m + 6)^2 = 17
Now, take the square root of both sides to solve for m:
m + 6 = ±√17
m = -6 ± √17
Therefore, the solutions to the equation m^2 + 12m + 19 = 0 are m = -6 + √17 and m = -6 - √17.