x^2+11x-9=0

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Solution for x^2+11x-9=0 equation: 


Simplifying
x2 + 11x + -9 = 0

Reorder the terms:
-9 + 11x + x2 = 0

Solving
-9 + 11x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '9' to each side of the equation.
-9 + 11x + 9 + x2 = 0 + 9

Reorder the terms:
-9 + 9 + 11x + x2 = 0 + 9

Combine like terms: -9 + 9 = 0
0 + 11x + x2 = 0 + 9
11x + x2 = 0 + 9

Combine like terms: 0 + 9 = 9
11x + x2 = 9

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 = 9 + 30.25

Reorder the terms:
30.25 + 11x + x2 = 9 + 30.25

Combine like terms: 9 + 30.25 = 39.25
30.25 + 11x + x2 = 39.25

Factor a perfect square on the left side:
(x + 5.5)(x + 5.5) = 39.25

Calculate the square root of the right side: 6.264982043

Break this problem into two subproblems by setting 
(x + 5.5) equal to 6.264982043 and -6.264982043.


Subproblem 1
x + 5.5 = 6.264982043

Simplifying
x + 5.5 = 6.264982043

Reorder the terms:
5.5 + x = 6.264982043

Solving
5.5 + x = 6.264982043

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 = 6.264982043 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + x = 6.264982043 + -5.5
x = 6.264982043 + -5.5

Combine like terms: 6.264982043 + -5.5 = 0.764982043
x = 0.764982043

Simplifying
x = 0.764982043


Subproblem 2
x + 5.5 = -6.264982043

Simplifying
x + 5.5 = -6.264982043

Reorder the terms:
5.5 + x = -6.264982043

Solving
5.5 + x = -6.264982043

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 = -6.264982043 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + x = -6.264982043 + -5.5
x = -6.264982043 + -5.5

Combine like terms: -6.264982043 + -5.5 = -11.764982043
x = -11.764982043

Simplifying
x = -11.764982043


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.764982043, -11.764982043}

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