4x^2+120x-364=0

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Solution for 4x^2+120x-364=0 equation: 


Simplifying
4x2 + 120x + -364 = 0

Reorder the terms:
-364 + 120x + 4x2 = 0

Solving
-364 + 120x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-91 + 30x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-91 + 30x + x2)' equal to zero and attempt to solve:

Simplifying
-91 + 30x + x2 = 0

Solving
-91 + 30x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '91' to each side of the equation.
-91 + 30x + 91 + x2 = 0 + 91

Reorder the terms:
-91 + 91 + 30x + x2 = 0 + 91

Combine like terms: -91 + 91 = 0
0 + 30x + x2 = 0 + 91
30x + x2 = 0 + 91

Combine like terms: 0 + 91 = 91
30x + x2 = 91

The x term is 30x.  Take half its coefficient (15).
Square it (225) and add it to both sides.

Add '225' to each side of the equation.
30x + 225 + x2 = 91 + 225

Reorder the terms:
225 + 30x + x2 = 91 + 225

Combine like terms: 91 + 225 = 316
225 + 30x + x2 = 316

Factor a perfect square on the left side:
(x + 15)(x + 15) = 316

Calculate the square root of the right side: 17.776388835

Break this problem into two subproblems by setting 
(x + 15) equal to 17.776388835 and -17.776388835.


Subproblem 1
x + 15 = 17.776388835

Simplifying
x + 15 = 17.776388835

Reorder the terms:
15 + x = 17.776388835

Solving
15 + x = 17.776388835

Solving for variable 'x'.

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

Add '-15' to each side of the equation.
15 + -15 + x = 17.776388835 + -15

Combine like terms: 15 + -15 = 0
0 + x = 17.776388835 + -15
x = 17.776388835 + -15

Combine like terms: 17.776388835 + -15 = 2.776388835
x = 2.776388835

Simplifying
x = 2.776388835


Subproblem 2
x + 15 = -17.776388835

Simplifying
x + 15 = -17.776388835

Reorder the terms:
15 + x = -17.776388835

Solving
15 + x = -17.776388835

Solving for variable 'x'.

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

Add '-15' to each side of the equation.
15 + -15 + x = -17.776388835 + -15

Combine like terms: 15 + -15 = 0
0 + x = -17.776388835 + -15
x = -17.776388835 + -15

Combine like terms: -17.776388835 + -15 = -32.776388835
x = -32.776388835

Simplifying
x = -32.776388835


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.776388835, -32.776388835}
Solution
x = {2.776388835, -32.776388835}

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