-2x^2-120x+3600=0

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Solution for -2x^2-120x+3600=0 equation: 


Simplifying
-2x2 + -120x + 3600 = 0

Reorder the terms:
3600 + -120x + -2x2 = 0

Solving
3600 + -120x + -2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(1800 + -60x + -1x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(1800 + -60x + -1x2)' equal to zero and attempt to solve:

Simplifying
1800 + -60x + -1x2 = 0

Solving
1800 + -60x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-1800 + 60x + x2 = 0

Move the constant term to the right:

Add '1800' to each side of the equation.
-1800 + 60x + 1800 + x2 = 0 + 1800

Reorder the terms:
-1800 + 1800 + 60x + x2 = 0 + 1800

Combine like terms: -1800 + 1800 = 0
0 + 60x + x2 = 0 + 1800
60x + x2 = 0 + 1800

Combine like terms: 0 + 1800 = 1800
60x + x2 = 1800

The x term is 60x.  Take half its coefficient (30).
Square it (900) and add it to both sides.

Add '900' to each side of the equation.
60x + 900 + x2 = 1800 + 900

Reorder the terms:
900 + 60x + x2 = 1800 + 900

Combine like terms: 1800 + 900 = 2700
900 + 60x + x2 = 2700

Factor a perfect square on the left side:
(x + 30)(x + 30) = 2700

Calculate the square root of the right side: 51.961524227

Break this problem into two subproblems by setting 
(x + 30) equal to 51.961524227 and -51.961524227.


Subproblem 1
x + 30 = 51.961524227

Simplifying
x + 30 = 51.961524227

Reorder the terms:
30 + x = 51.961524227

Solving
30 + x = 51.961524227

Solving for variable 'x'.

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

Add '-30' to each side of the equation.
30 + -30 + x = 51.961524227 + -30

Combine like terms: 30 + -30 = 0
0 + x = 51.961524227 + -30
x = 51.961524227 + -30

Combine like terms: 51.961524227 + -30 = 21.961524227
x = 21.961524227

Simplifying
x = 21.961524227


Subproblem 2
x + 30 = -51.961524227

Simplifying
x + 30 = -51.961524227

Reorder the terms:
30 + x = -51.961524227

Solving
30 + x = -51.961524227

Solving for variable 'x'.

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

Add '-30' to each side of the equation.
30 + -30 + x = -51.961524227 + -30

Combine like terms: 30 + -30 = 0
0 + x = -51.961524227 + -30
x = -51.961524227 + -30

Combine like terms: -51.961524227 + -30 = -81.961524227
x = -81.961524227

Simplifying
x = -81.961524227


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {21.961524227, -81.961524227}
Solution
x = {21.961524227, -81.961524227}

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