x^2+120x+720=0

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Solution for x^2+120x+720=0 equation: 


Simplifying
x2 + 120x + 720 = 0

Reorder the terms:
720 + 120x + x2 = 0

Solving
720 + 120x + 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 + 120x + -720 + x2 = 0 + -720

Reorder the terms:
720 + -720 + 120x + x2 = 0 + -720

Combine like terms: 720 + -720 = 0
0 + 120x + x2 = 0 + -720
120x + x2 = 0 + -720

Combine like terms: 0 + -720 = -720
120x + x2 = -720

The x term is 120x.  Take half its coefficient (60).
Square it (3600) and add it to both sides.

Add '3600' to each side of the equation.
120x + 3600 + x2 = -720 + 3600

Reorder the terms:
3600 + 120x + x2 = -720 + 3600

Combine like terms: -720 + 3600 = 2880
3600 + 120x + x2 = 2880

Factor a perfect square on the left side:
(x + 60)(x + 60) = 2880

Calculate the square root of the right side: 53.66563146

Break this problem into two subproblems by setting 
(x + 60) equal to 53.66563146 and -53.66563146.


Subproblem 1
x + 60 = 53.66563146

Simplifying
x + 60 = 53.66563146

Reorder the terms:
60 + x = 53.66563146

Solving
60 + x = 53.66563146

Solving for variable 'x'.

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

Add '-60' to each side of the equation.
60 + -60 + x = 53.66563146 + -60

Combine like terms: 60 + -60 = 0
0 + x = 53.66563146 + -60
x = 53.66563146 + -60

Combine like terms: 53.66563146 + -60 = -6.33436854
x = -6.33436854

Simplifying
x = -6.33436854


Subproblem 2
x + 60 = -53.66563146

Simplifying
x + 60 = -53.66563146

Reorder the terms:
60 + x = -53.66563146

Solving
60 + x = -53.66563146

Solving for variable 'x'.

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

Add '-60' to each side of the equation.
60 + -60 + x = -53.66563146 + -60

Combine like terms: 60 + -60 = 0
0 + x = -53.66563146 + -60
x = -53.66563146 + -60

Combine like terms: -53.66563146 + -60 = -113.66563146
x = -113.66563146

Simplifying
x = -113.66563146


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-6.33436854, -113.66563146}

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