x^2+11x-114=0

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Solution for x^2+11x-114=0 equation: 


Simplifying
x2 + 11x + -114 = 0

Reorder the terms:
-114 + 11x + x2 = 0

Solving
-114 + 11x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '114' to each side of the equation.
-114 + 11x + 114 + x2 = 0 + 114

Reorder the terms:
-114 + 114 + 11x + x2 = 0 + 114

Combine like terms: -114 + 114 = 0
0 + 11x + x2 = 0 + 114
11x + x2 = 0 + 114

Combine like terms: 0 + 114 = 114
11x + x2 = 114

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 = 114 + 30.25

Reorder the terms:
30.25 + 11x + x2 = 114 + 30.25

Combine like terms: 114 + 30.25 = 144.25
30.25 + 11x + x2 = 144.25

Factor a perfect square on the left side:
(x + 5.5)(x + 5.5) = 144.25

Calculate the square root of the right side: 12.010412149

Break this problem into two subproblems by setting 
(x + 5.5) equal to 12.010412149 and -12.010412149.


Subproblem 1
x + 5.5 = 12.010412149

Simplifying
x + 5.5 = 12.010412149

Reorder the terms:
5.5 + x = 12.010412149

Solving
5.5 + x = 12.010412149

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 = 12.010412149 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + x = 12.010412149 + -5.5
x = 12.010412149 + -5.5

Combine like terms: 12.010412149 + -5.5 = 6.510412149
x = 6.510412149

Simplifying
x = 6.510412149


Subproblem 2
x + 5.5 = -12.010412149

Simplifying
x + 5.5 = -12.010412149

Reorder the terms:
5.5 + x = -12.010412149

Solving
5.5 + x = -12.010412149

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 = -12.010412149 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + x = -12.010412149 + -5.5
x = -12.010412149 + -5.5

Combine like terms: -12.010412149 + -5.5 = -17.510412149
x = -17.510412149

Simplifying
x = -17.510412149


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.510412149, -17.510412149}

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