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Simplifying
x2 + 5x + 6 = 0

Reorder the terms:
6 + 5x + x2 = 0

Solving
6 + 5x + x2 = 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 + x2 = 0 + -6

Reorder the terms:
6 + -6 + 5x + x2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 5x + x2 = 0 + -6
5x + x2 = 0 + -6

Combine like terms: 0 + -6 = -6
5x + x2 = -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 + x2 = -6 + 6.25

Reorder the terms:
6.25 + 5x + x2 = -6 + 6.25

Combine like terms: -6 + 6.25 = 0.25
6.25 + 5x + x2 = 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}
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