Solve x^2 + 6x + 5 = 0 by completing the square.
Solution
Problem
Solve x^2 + 6x + 5 = 0 by completing the square.
Start with:
x^2 + 6x + 5 = 0
Move the constant term to the other side:
x^2 + 6x = -5
To complete the square, take half of the coefficient of x and square it:
(6/2)^2 = 9
Add 9 to both sides:
x^2 + 6x + 9 = 4
The left side is now a perfect square:
(x + 3)^2 = 4
Take the square root of both sides:
x + 3 = 2 or x + 3 = -2
Solve each equation:
x = -1 or x = -5
Result
x = -1, -5