x^2-27x-80=0

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Solution for x^2-27x-80=0 equation: 


Simplifying
x2 + -27x + -80 = 0

Reorder the terms:
-80 + -27x + x2 = 0

Solving
-80 + -27x + 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 + -27x + 80 + x2 = 0 + 80

Reorder the terms:
-80 + 80 + -27x + x2 = 0 + 80

Combine like terms: -80 + 80 = 0
0 + -27x + x2 = 0 + 80
-27x + x2 = 0 + 80

Combine like terms: 0 + 80 = 80
-27x + x2 = 80

The x term is -27x.  Take half its coefficient (-13.5).
Square it (182.25) and add it to both sides.

Add '182.25' to each side of the equation.
-27x + 182.25 + x2 = 80 + 182.25

Reorder the terms:
182.25 + -27x + x2 = 80 + 182.25

Combine like terms: 80 + 182.25 = 262.25
182.25 + -27x + x2 = 262.25

Factor a perfect square on the left side:
(x + -13.5)(x + -13.5) = 262.25

Calculate the square root of the right side: 16.194134741

Break this problem into two subproblems by setting 
(x + -13.5) equal to 16.194134741 and -16.194134741.


Subproblem 1
x + -13.5 = 16.194134741

Simplifying
x + -13.5 = 16.194134741

Reorder the terms:
-13.5 + x = 16.194134741

Solving
-13.5 + x = 16.194134741

Solving for variable 'x'.

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

Add '13.5' to each side of the equation.
-13.5 + 13.5 + x = 16.194134741 + 13.5

Combine like terms: -13.5 + 13.5 = 0.0
0.0 + x = 16.194134741 + 13.5
x = 16.194134741 + 13.5

Combine like terms: 16.194134741 + 13.5 = 29.694134741
x = 29.694134741

Simplifying
x = 29.694134741


Subproblem 2
x + -13.5 = -16.194134741

Simplifying
x + -13.5 = -16.194134741

Reorder the terms:
-13.5 + x = -16.194134741

Solving
-13.5 + x = -16.194134741

Solving for variable 'x'.

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

Add '13.5' to each side of the equation.
-13.5 + 13.5 + x = -16.194134741 + 13.5

Combine like terms: -13.5 + 13.5 = 0.0
0.0 + x = -16.194134741 + 13.5
x = -16.194134741 + 13.5

Combine like terms: -16.194134741 + 13.5 = -2.694134741
x = -2.694134741

Simplifying
x = -2.694134741


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {29.694134741, -2.694134741}

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