x^2-29x-80=0

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Solution for x^2-29x-80=0 equation: 


Simplifying
x2 + -29x + -80 = 0

Reorder the terms:
-80 + -29x + x2 = 0

Solving
-80 + -29x + 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 + -29x + 80 + x2 = 0 + 80

Reorder the terms:
-80 + 80 + -29x + x2 = 0 + 80

Combine like terms: -80 + 80 = 0
0 + -29x + x2 = 0 + 80
-29x + x2 = 0 + 80

Combine like terms: 0 + 80 = 80
-29x + x2 = 80

The x term is -29x.  Take half its coefficient (-14.5).
Square it (210.25) and add it to both sides.

Add '210.25' to each side of the equation.
-29x + 210.25 + x2 = 80 + 210.25

Reorder the terms:
210.25 + -29x + x2 = 80 + 210.25

Combine like terms: 80 + 210.25 = 290.25
210.25 + -29x + x2 = 290.25

Factor a perfect square on the left side:
(x + -14.5)(x + -14.5) = 290.25

Calculate the square root of the right side: 17.036725037

Break this problem into two subproblems by setting 
(x + -14.5) equal to 17.036725037 and -17.036725037.


Subproblem 1
x + -14.5 = 17.036725037

Simplifying
x + -14.5 = 17.036725037

Reorder the terms:
-14.5 + x = 17.036725037

Solving
-14.5 + x = 17.036725037

Solving for variable 'x'.

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

Add '14.5' to each side of the equation.
-14.5 + 14.5 + x = 17.036725037 + 14.5

Combine like terms: -14.5 + 14.5 = 0.0
0.0 + x = 17.036725037 + 14.5
x = 17.036725037 + 14.5

Combine like terms: 17.036725037 + 14.5 = 31.536725037
x = 31.536725037

Simplifying
x = 31.536725037


Subproblem 2
x + -14.5 = -17.036725037

Simplifying
x + -14.5 = -17.036725037

Reorder the terms:
-14.5 + x = -17.036725037

Solving
-14.5 + x = -17.036725037

Solving for variable 'x'.

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

Add '14.5' to each side of the equation.
-14.5 + 14.5 + x = -17.036725037 + 14.5

Combine like terms: -14.5 + 14.5 = 0.0
0.0 + x = -17.036725037 + 14.5
x = -17.036725037 + 14.5

Combine like terms: -17.036725037 + 14.5 = -2.536725037
x = -2.536725037

Simplifying
x = -2.536725037


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {31.536725037, -2.536725037}

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