x^2-13x-180=0

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Solution for x^2-13x-180=0 equation: 


Simplifying
x2 + -13x + -180 = 0

Reorder the terms:
-180 + -13x + x2 = 0

Solving
-180 + -13x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '180' to each side of the equation.
-180 + -13x + 180 + x2 = 0 + 180

Reorder the terms:
-180 + 180 + -13x + x2 = 0 + 180

Combine like terms: -180 + 180 = 0
0 + -13x + x2 = 0 + 180
-13x + x2 = 0 + 180

Combine like terms: 0 + 180 = 180
-13x + x2 = 180

The x term is -13x.  Take half its coefficient (-6.5).
Square it (42.25) and add it to both sides.

Add '42.25' to each side of the equation.
-13x + 42.25 + x2 = 180 + 42.25

Reorder the terms:
42.25 + -13x + x2 = 180 + 42.25

Combine like terms: 180 + 42.25 = 222.25
42.25 + -13x + x2 = 222.25

Factor a perfect square on the left side:
(x + -6.5)(x + -6.5) = 222.25

Calculate the square root of the right side: 14.908051516

Break this problem into two subproblems by setting 
(x + -6.5) equal to 14.908051516 and -14.908051516.


Subproblem 1
x + -6.5 = 14.908051516

Simplifying
x + -6.5 = 14.908051516

Reorder the terms:
-6.5 + x = 14.908051516

Solving
-6.5 + x = 14.908051516

Solving for variable 'x'.

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

Add '6.5' to each side of the equation.
-6.5 + 6.5 + x = 14.908051516 + 6.5

Combine like terms: -6.5 + 6.5 = 0.0
0.0 + x = 14.908051516 + 6.5
x = 14.908051516 + 6.5

Combine like terms: 14.908051516 + 6.5 = 21.408051516
x = 21.408051516

Simplifying
x = 21.408051516


Subproblem 2
x + -6.5 = -14.908051516

Simplifying
x + -6.5 = -14.908051516

Reorder the terms:
-6.5 + x = -14.908051516

Solving
-6.5 + x = -14.908051516

Solving for variable 'x'.

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

Add '6.5' to each side of the equation.
-6.5 + 6.5 + x = -14.908051516 + 6.5

Combine like terms: -6.5 + 6.5 = 0.0
0.0 + x = -14.908051516 + 6.5
x = -14.908051516 + 6.5

Combine like terms: -14.908051516 + 6.5 = -8.408051516
x = -8.408051516

Simplifying
x = -8.408051516


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {21.408051516, -8.408051516}

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