Solve x^2 + 6x + 5 = 0 by completing the square.

Solution

Algebra · Medium

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