x^2+11x+8=-4

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Solution for x^2+11x+8=-4 equation:


Simplifying
x2 + 11x + 8 = -4

Reorder the terms:
8 + 11x + x2 = -4

Solving
8 + 11x + x2 = -4

Solving for variable 'x'.

Reorder the terms:
8 + 4 + 11x + x2 = -4 + 4

Combine like terms: 8 + 4 = 12
12 + 11x + x2 = -4 + 4

Combine like terms: -4 + 4 = 0
12 + 11x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-12' to each side of the equation.
12 + 11x + -12 + x2 = 0 + -12

Reorder the terms:
12 + -12 + 11x + x2 = 0 + -12

Combine like terms: 12 + -12 = 0
0 + 11x + x2 = 0 + -12
11x + x2 = 0 + -12

Combine like terms: 0 + -12 = -12
11x + x2 = -12

The x term is 11x.  Take half its coefficient (5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
11x + 30.25 + x2 = -12 + 30.25

Reorder the terms:
30.25 + 11x + x2 = -12 + 30.25

Combine like terms: -12 + 30.25 = 18.25
30.25 + 11x + x2 = 18.25

Factor a perfect square on the left side:
(x + 5.5)(x + 5.5) = 18.25

Calculate the square root of the right side: 4.272001873

Break this problem into two subproblems by setting 
(x + 5.5) equal to 4.272001873 and -4.272001873.

Subproblem 1

x + 5.5 = 4.272001873 Simplifying x + 5.5 = 4.272001873 Reorder the terms: 5.5 + x = 4.272001873 Solving 5.5 + x = 4.272001873 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + x = 4.272001873 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = 4.272001873 + -5.5 x = 4.272001873 + -5.5 Combine like terms: 4.272001873 + -5.5 = -1.227998127 x = -1.227998127 Simplifying x = -1.227998127

Subproblem 2

x + 5.5 = -4.272001873 Simplifying x + 5.5 = -4.272001873 Reorder the terms: 5.5 + x = -4.272001873 Solving 5.5 + x = -4.272001873 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + x = -4.272001873 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = -4.272001873 + -5.5 x = -4.272001873 + -5.5 Combine like terms: -4.272001873 + -5.5 = -9.772001873 x = -9.772001873 Simplifying x = -9.772001873

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-1.227998127, -9.772001873}

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