x^2+10x-113.09=

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Solution for x^2+10x-113.09= equation: 


Simplifying
x2 + 10x + -113.09 = 0

Reorder the terms:
-113.09 + 10x + x2 = 0

Solving
-113.09 + 10x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '113.09' to each side of the equation.
-113.09 + 10x + 113.09 + x2 = 0 + 113.09

Reorder the terms:
-113.09 + 113.09 + 10x + x2 = 0 + 113.09

Combine like terms: -113.09 + 113.09 = 0.00
0.00 + 10x + x2 = 0 + 113.09
10x + x2 = 0 + 113.09

Combine like terms: 0 + 113.09 = 113.09
10x + x2 = 113.09

The x term is 10x.  Take half its coefficient (5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
10x + 25 + x2 = 113.09 + 25

Reorder the terms:
25 + 10x + x2 = 113.09 + 25

Combine like terms: 113.09 + 25 = 138.09
25 + 10x + x2 = 138.09

Factor a perfect square on the left side:
(x + 5)(x + 5) = 138.09

Calculate the square root of the right side: 11.751170155

Break this problem into two subproblems by setting 
(x + 5) equal to 11.751170155 and -11.751170155.


Subproblem 1
x + 5 = 11.751170155

Simplifying
x + 5 = 11.751170155

Reorder the terms:
5 + x = 11.751170155

Solving
5 + x = 11.751170155

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-5' to each side of the equation.
5 + -5 + x = 11.751170155 + -5

Combine like terms: 5 + -5 = 0
0 + x = 11.751170155 + -5
x = 11.751170155 + -5

Combine like terms: 11.751170155 + -5 = 6.751170155
x = 6.751170155

Simplifying
x = 6.751170155


Subproblem 2
x + 5 = -11.751170155

Simplifying
x + 5 = -11.751170155

Reorder the terms:
5 + x = -11.751170155

Solving
5 + x = -11.751170155

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-5' to each side of the equation.
5 + -5 + x = -11.751170155 + -5

Combine like terms: 5 + -5 = 0
0 + x = -11.751170155 + -5
x = -11.751170155 + -5

Combine like terms: -11.751170155 + -5 = -16.751170155
x = -16.751170155

Simplifying
x = -16.751170155


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.751170155, -16.751170155}

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