x^2-5x-6-100=0

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Solution for x^2-5x-6-100=0 equation: 


Simplifying
x2 + -5x + -6 + -100 = 0

Reorder the terms:
-6 + -100 + -5x + x2 = 0

Combine like terms: -6 + -100 = -106
-106 + -5x + x2 = 0

Solving
-106 + -5x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '106' to each side of the equation.
-106 + -5x + 106 + x2 = 0 + 106

Reorder the terms:
-106 + 106 + -5x + x2 = 0 + 106

Combine like terms: -106 + 106 = 0
0 + -5x + x2 = 0 + 106
-5x + x2 = 0 + 106

Combine like terms: 0 + 106 = 106
-5x + x2 = 106

The x term is -5x.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5x + 6.25 + x2 = 106 + 6.25

Reorder the terms:
6.25 + -5x + x2 = 106 + 6.25

Combine like terms: 106 + 6.25 = 112.25
6.25 + -5x + x2 = 112.25

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 112.25

Calculate the square root of the right side: 10.59481005

Break this problem into two subproblems by setting 
(x + -2.5) equal to 10.59481005 and -10.59481005.


Subproblem 1
x + -2.5 = 10.59481005

Simplifying
x + -2.5 = 10.59481005

Reorder the terms:
-2.5 + x = 10.59481005

Solving
-2.5 + x = 10.59481005

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = 10.59481005 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = 10.59481005 + 2.5
x = 10.59481005 + 2.5

Combine like terms: 10.59481005 + 2.5 = 13.09481005
x = 13.09481005

Simplifying
x = 13.09481005


Subproblem 2
x + -2.5 = -10.59481005

Simplifying
x + -2.5 = -10.59481005

Reorder the terms:
-2.5 + x = -10.59481005

Solving
-2.5 + x = -10.59481005

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = -10.59481005 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = -10.59481005 + 2.5
x = -10.59481005 + 2.5

Combine like terms: -10.59481005 + 2.5 = -8.09481005
x = -8.09481005

Simplifying
x = -8.09481005


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {13.09481005, -8.09481005}

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