x^2-15x-80=0

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Solution for x^2-15x-80=0 equation: 


Simplifying
x2 + -15x + -80 = 0

Reorder the terms:
-80 + -15x + x2 = 0

Solving
-80 + -15x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '80' to each side of the equation.
-80 + -15x + 80 + x2 = 0 + 80

Reorder the terms:
-80 + 80 + -15x + x2 = 0 + 80

Combine like terms: -80 + 80 = 0
0 + -15x + x2 = 0 + 80
-15x + x2 = 0 + 80

Combine like terms: 0 + 80 = 80
-15x + x2 = 80

The x term is -15x.  Take half its coefficient (-7.5).
Square it (56.25) and add it to both sides.

Add '56.25' to each side of the equation.
-15x + 56.25 + x2 = 80 + 56.25

Reorder the terms:
56.25 + -15x + x2 = 80 + 56.25

Combine like terms: 80 + 56.25 = 136.25
56.25 + -15x + x2 = 136.25

Factor a perfect square on the left side:
(x + -7.5)(x + -7.5) = 136.25

Calculate the square root of the right side: 11.67261753

Break this problem into two subproblems by setting 
(x + -7.5) equal to 11.67261753 and -11.67261753.


Subproblem 1
x + -7.5 = 11.67261753

Simplifying
x + -7.5 = 11.67261753

Reorder the terms:
-7.5 + x = 11.67261753

Solving
-7.5 + x = 11.67261753

Solving for variable 'x'.

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

Add '7.5' to each side of the equation.
-7.5 + 7.5 + x = 11.67261753 + 7.5

Combine like terms: -7.5 + 7.5 = 0.0
0.0 + x = 11.67261753 + 7.5
x = 11.67261753 + 7.5

Combine like terms: 11.67261753 + 7.5 = 19.17261753
x = 19.17261753

Simplifying
x = 19.17261753


Subproblem 2
x + -7.5 = -11.67261753

Simplifying
x + -7.5 = -11.67261753

Reorder the terms:
-7.5 + x = -11.67261753

Solving
-7.5 + x = -11.67261753

Solving for variable 'x'.

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

Add '7.5' to each side of the equation.
-7.5 + 7.5 + x = -11.67261753 + 7.5

Combine like terms: -7.5 + 7.5 = 0.0
0.0 + x = -11.67261753 + 7.5
x = -11.67261753 + 7.5

Combine like terms: -11.67261753 + 7.5 = -4.17261753
x = -4.17261753

Simplifying
x = -4.17261753


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {19.17261753, -4.17261753}

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