3x^2-240x-3600=0

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Solution for 3x^2-240x-3600=0 equation: 


Simplifying
3x2 + -240x + -3600 = 0

Reorder the terms:
-3600 + -240x + 3x2 = 0

Solving
-3600 + -240x + 3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-1200 + -80x + x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-1200 + -80x + x2)' equal to zero and attempt to solve:

Simplifying
-1200 + -80x + x2 = 0

Solving
-1200 + -80x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '1200' to each side of the equation.
-1200 + -80x + 1200 + x2 = 0 + 1200

Reorder the terms:
-1200 + 1200 + -80x + x2 = 0 + 1200

Combine like terms: -1200 + 1200 = 0
0 + -80x + x2 = 0 + 1200
-80x + x2 = 0 + 1200

Combine like terms: 0 + 1200 = 1200
-80x + x2 = 1200

The x term is -80x.  Take half its coefficient (-40).
Square it (1600) and add it to both sides.

Add '1600' to each side of the equation.
-80x + 1600 + x2 = 1200 + 1600

Reorder the terms:
1600 + -80x + x2 = 1200 + 1600

Combine like terms: 1200 + 1600 = 2800
1600 + -80x + x2 = 2800

Factor a perfect square on the left side:
(x + -40)(x + -40) = 2800

Calculate the square root of the right side: 52.915026221

Break this problem into two subproblems by setting 
(x + -40) equal to 52.915026221 and -52.915026221.


Subproblem 1
x + -40 = 52.915026221

Simplifying
x + -40 = 52.915026221

Reorder the terms:
-40 + x = 52.915026221

Solving
-40 + x = 52.915026221

Solving for variable 'x'.

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

Add '40' to each side of the equation.
-40 + 40 + x = 52.915026221 + 40

Combine like terms: -40 + 40 = 0
0 + x = 52.915026221 + 40
x = 52.915026221 + 40

Combine like terms: 52.915026221 + 40 = 92.915026221
x = 92.915026221

Simplifying
x = 92.915026221


Subproblem 2
x + -40 = -52.915026221

Simplifying
x + -40 = -52.915026221

Reorder the terms:
-40 + x = -52.915026221

Solving
-40 + x = -52.915026221

Solving for variable 'x'.

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

Add '40' to each side of the equation.
-40 + 40 + x = -52.915026221 + 40

Combine like terms: -40 + 40 = 0
0 + x = -52.915026221 + 40
x = -52.915026221 + 40

Combine like terms: -52.915026221 + 40 = -12.915026221
x = -12.915026221

Simplifying
x = -12.915026221


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {92.915026221, -12.915026221}
Solution
x = {92.915026221, -12.915026221}

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