Simplifying
x^{2} + 5x + 6 = 0
Reorder the terms:
6 + 5x + x^{2} = 0
Solving
6 + 5x + x^{2} = 0
Solving for variable 'x'.
Begin completing the square.
Move the constant term to the right:
Add '-6' to each side of the equation.
6 + 5x + -6 + x^{2} = 0 + -6
Reorder the terms:
6 + -6 + 5x + x^{2} = 0 + -6
Combine like terms: 6 + -6 = 0
0 + 5x + x^{2} = 0 + -6
5x + x^{2} = 0 + -6
Combine like terms: 0 + -6 = -6
5x + x^{2} = -6
The x term is 5x. Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.
Add '6.25' to each side of the equation.
5x + 6.25 + x^{2} = -6 + 6.25
Reorder the terms:
6.25 + 5x + x^{2} = -6 + 6.25
Combine like terms: -6 + 6.25 = 0.25
6.25 + 5x + x^{2} = 0.25
Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 0.25
Calculate the square root of the right side: 0.5
Break this problem into two subproblems by setting
(x + 2.5) equal to 0.5 and -0.5.
#### Subproblem 1

x + 2.5 = 0.5
Simplifying
x + 2.5 = 0.5
Reorder the terms:
2.5 + x = 0.5
Solving
2.5 + x = 0.5
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = 0.5 + -2.5
Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 0.5 + -2.5
x = 0.5 + -2.5
Combine like terms: 0.5 + -2.5 = -2
x = -2
Simplifying
x = -2
#### Subproblem 2

x + 2.5 = -0.5
Simplifying
x + 2.5 = -0.5
Reorder the terms:
2.5 + x = -0.5
Solving
2.5 + x = -0.5
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = -0.5 + -2.5
Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -0.5 + -2.5
x = -0.5 + -2.5
Combine like terms: -0.5 + -2.5 = -3
x = -3
Simplifying
x = -3
#### Solution

The solution to the problem is based on the solutions
from the subproblems.
x = {-2, -3}