x^2+11x+7=0

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Solution for x^2+11x+7=0 equation: 


Simplifying
x2 + 11x + 7 = 0

Reorder the terms:
7 + 11x + x2 = 0

Solving
7 + 11x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-7' to each side of the equation.
7 + 11x + -7 + x2 = 0 + -7

Reorder the terms:
7 + -7 + 11x + x2 = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 11x + x2 = 0 + -7
11x + x2 = 0 + -7

Combine like terms: 0 + -7 = -7
11x + x2 = -7

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 = -7 + 30.25

Reorder the terms:
30.25 + 11x + x2 = -7 + 30.25

Combine like terms: -7 + 30.25 = 23.25
30.25 + 11x + x2 = 23.25

Factor a perfect square on the left side:
(x + 5.5)(x + 5.5) = 23.25

Calculate the square root of the right side: 4.82182538

Break this problem into two subproblems by setting 
(x + 5.5) equal to 4.82182538 and -4.82182538.


Subproblem 1
x + 5.5 = 4.82182538

Simplifying
x + 5.5 = 4.82182538

Reorder the terms:
5.5 + x = 4.82182538

Solving
5.5 + x = 4.82182538

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 = 4.82182538 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + x = 4.82182538 + -5.5
x = 4.82182538 + -5.5

Combine like terms: 4.82182538 + -5.5 = -0.67817462
x = -0.67817462

Simplifying
x = -0.67817462


Subproblem 2
x + 5.5 = -4.82182538

Simplifying
x + 5.5 = -4.82182538

Reorder the terms:
5.5 + x = -4.82182538

Solving
5.5 + x = -4.82182538

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 = -4.82182538 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + x = -4.82182538 + -5.5
x = -4.82182538 + -5.5

Combine like terms: -4.82182538 + -5.5 = -10.32182538
x = -10.32182538

Simplifying
x = -10.32182538


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.67817462, -10.32182538}

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