3x^2+360x-4=0

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Solution for 3x^2+360x-4=0 equation: 


Simplifying
3x2 + 360x + -4 = 0

Reorder the terms:
-4 + 360x + 3x2 = 0

Solving
-4 + 360x + 3x2 = 0

Solving for variable 'x'.

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

Divide each side by '3'.
-1.333333333 + 120x + x2 = 0

Move the constant term to the right:

Add '1.333333333' to each side of the equation.
-1.333333333 + 120x + 1.333333333 + x2 = 0 + 1.333333333

Reorder the terms:
-1.333333333 + 1.333333333 + 120x + x2 = 0 + 1.333333333

Combine like terms: -1.333333333 + 1.333333333 = 0.000000000
0.000000000 + 120x + x2 = 0 + 1.333333333
120x + x2 = 0 + 1.333333333

Combine like terms: 0 + 1.333333333 = 1.333333333
120x + x2 = 1.333333333

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 = 1.333333333 + 3600

Reorder the terms:
3600 + 120x + x2 = 1.333333333 + 3600

Combine like terms: 1.333333333 + 3600 = 3601.333333333
3600 + 120x + x2 = 3601.333333333

Factor a perfect square on the left side:
(x + 60)(x + 60) = 3601.333333333

Calculate the square root of the right side: 60.011110082

Break this problem into two subproblems by setting 
(x + 60) equal to 60.011110082 and -60.011110082.


Subproblem 1
x + 60 = 60.011110082

Simplifying
x + 60 = 60.011110082

Reorder the terms:
60 + x = 60.011110082

Solving
60 + x = 60.011110082

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 = 60.011110082 + -60

Combine like terms: 60 + -60 = 0
0 + x = 60.011110082 + -60
x = 60.011110082 + -60

Combine like terms: 60.011110082 + -60 = 0.011110082
x = 0.011110082

Simplifying
x = 0.011110082


Subproblem 2
x + 60 = -60.011110082

Simplifying
x + 60 = -60.011110082

Reorder the terms:
60 + x = -60.011110082

Solving
60 + x = -60.011110082

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 = -60.011110082 + -60

Combine like terms: 60 + -60 = 0
0 + x = -60.011110082 + -60
x = -60.011110082 + -60

Combine like terms: -60.011110082 + -60 = -120.011110082
x = -120.011110082

Simplifying
x = -120.011110082


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.011110082, -120.011110082}

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