x^2+72x-720=0

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Solution for x^2+72x-720=0 equation: 


Simplifying
x2 + 72x + -720 = 0

Reorder the terms:
-720 + 72x + x2 = 0

Solving
-720 + 72x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '720' to each side of the equation.
-720 + 72x + 720 + x2 = 0 + 720

Reorder the terms:
-720 + 720 + 72x + x2 = 0 + 720

Combine like terms: -720 + 720 = 0
0 + 72x + x2 = 0 + 720
72x + x2 = 0 + 720

Combine like terms: 0 + 720 = 720
72x + x2 = 720

The x term is 72x.  Take half its coefficient (36).
Square it (1296) and add it to both sides.

Add '1296' to each side of the equation.
72x + 1296 + x2 = 720 + 1296

Reorder the terms:
1296 + 72x + x2 = 720 + 1296

Combine like terms: 720 + 1296 = 2016
1296 + 72x + x2 = 2016

Factor a perfect square on the left side:
(x + 36)(x + 36) = 2016

Calculate the square root of the right side: 44.899888641

Break this problem into two subproblems by setting 
(x + 36) equal to 44.899888641 and -44.899888641.


Subproblem 1
x + 36 = 44.899888641

Simplifying
x + 36 = 44.899888641

Reorder the terms:
36 + x = 44.899888641

Solving
36 + x = 44.899888641

Solving for variable 'x'.

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

Add '-36' to each side of the equation.
36 + -36 + x = 44.899888641 + -36

Combine like terms: 36 + -36 = 0
0 + x = 44.899888641 + -36
x = 44.899888641 + -36

Combine like terms: 44.899888641 + -36 = 8.899888641
x = 8.899888641

Simplifying
x = 8.899888641


Subproblem 2
x + 36 = -44.899888641

Simplifying
x + 36 = -44.899888641

Reorder the terms:
36 + x = -44.899888641

Solving
36 + x = -44.899888641

Solving for variable 'x'.

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

Add '-36' to each side of the equation.
36 + -36 + x = -44.899888641 + -36

Combine like terms: 36 + -36 = 0
0 + x = -44.899888641 + -36
x = -44.899888641 + -36

Combine like terms: -44.899888641 + -36 = -80.899888641
x = -80.899888641

Simplifying
x = -80.899888641


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.899888641, -80.899888641}

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