4x^2+66x-236=0

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Solution for 4x^2+66x-236=0 equation: 


Simplifying
4x2 + 66x + -236 = 0

Reorder the terms:
-236 + 66x + 4x2 = 0

Solving
-236 + 66x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-118 + 33x + 2x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-118 + 33x + 2x2)' equal to zero and attempt to solve:

Simplifying
-118 + 33x + 2x2 = 0

Solving
-118 + 33x + 2x2 = 0

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

Divide each side by '2'.
-59 + 16.5x + x2 = 0

Move the constant term to the right:

Add '59' to each side of the equation.
-59 + 16.5x + 59 + x2 = 0 + 59

Reorder the terms:
-59 + 59 + 16.5x + x2 = 0 + 59

Combine like terms: -59 + 59 = 0
0 + 16.5x + x2 = 0 + 59
16.5x + x2 = 0 + 59

Combine like terms: 0 + 59 = 59
16.5x + x2 = 59

The x term is 16.5x.  Take half its coefficient (8.25).
Square it (68.0625) and add it to both sides.

Add '68.0625' to each side of the equation.
16.5x + 68.0625 + x2 = 59 + 68.0625

Reorder the terms:
68.0625 + 16.5x + x2 = 59 + 68.0625

Combine like terms: 59 + 68.0625 = 127.0625
68.0625 + 16.5x + x2 = 127.0625

Factor a perfect square on the left side:
(x + 8.25)(x + 8.25) = 127.0625

Calculate the square root of the right side: 11.272200318

Break this problem into two subproblems by setting 
(x + 8.25) equal to 11.272200318 and -11.272200318.


Subproblem 1
x + 8.25 = 11.272200318

Simplifying
x + 8.25 = 11.272200318

Reorder the terms:
8.25 + x = 11.272200318

Solving
8.25 + x = 11.272200318

Solving for variable 'x'.

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

Add '-8.25' to each side of the equation.
8.25 + -8.25 + x = 11.272200318 + -8.25

Combine like terms: 8.25 + -8.25 = 0.00
0.00 + x = 11.272200318 + -8.25
x = 11.272200318 + -8.25

Combine like terms: 11.272200318 + -8.25 = 3.022200318
x = 3.022200318

Simplifying
x = 3.022200318


Subproblem 2
x + 8.25 = -11.272200318

Simplifying
x + 8.25 = -11.272200318

Reorder the terms:
8.25 + x = -11.272200318

Solving
8.25 + x = -11.272200318

Solving for variable 'x'.

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

Add '-8.25' to each side of the equation.
8.25 + -8.25 + x = -11.272200318 + -8.25

Combine like terms: 8.25 + -8.25 = 0.00
0.00 + x = -11.272200318 + -8.25
x = -11.272200318 + -8.25

Combine like terms: -11.272200318 + -8.25 = -19.522200318
x = -19.522200318

Simplifying
x = -19.522200318


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.022200318, -19.522200318}
Solution
x = {3.022200318, -19.522200318}

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