4x^2+4x-180=0

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Solution for 4x^2+4x-180=0 equation: 


Simplifying
4x2 + 4x + -180 = 0

Reorder the terms:
-180 + 4x + 4x2 = 0

Solving
-180 + 4x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-45 + x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-45 + x + x2)' equal to zero and attempt to solve:

Simplifying
-45 + x + x2 = 0

Solving
-45 + x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '45' to each side of the equation.
-45 + x + 45 + x2 = 0 + 45

Reorder the terms:
-45 + 45 + x + x2 = 0 + 45

Combine like terms: -45 + 45 = 0
0 + x + x2 = 0 + 45
x + x2 = 0 + 45

Combine like terms: 0 + 45 = 45
x + x2 = 45

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
x + 0.25 + x2 = 45 + 0.25

Reorder the terms:
0.25 + x + x2 = 45 + 0.25

Combine like terms: 45 + 0.25 = 45.25
0.25 + x + x2 = 45.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 45.25

Calculate the square root of the right side: 6.726812024

Break this problem into two subproblems by setting 
(x + 0.5) equal to 6.726812024 and -6.726812024.


Subproblem 1
x + 0.5 = 6.726812024

Simplifying
x + 0.5 = 6.726812024

Reorder the terms:
0.5 + x = 6.726812024

Solving
0.5 + x = 6.726812024

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 6.726812024 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 6.726812024 + -0.5
x = 6.726812024 + -0.5

Combine like terms: 6.726812024 + -0.5 = 6.226812024
x = 6.226812024

Simplifying
x = 6.226812024


Subproblem 2
x + 0.5 = -6.726812024

Simplifying
x + 0.5 = -6.726812024

Reorder the terms:
0.5 + x = -6.726812024

Solving
0.5 + x = -6.726812024

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -6.726812024 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -6.726812024 + -0.5
x = -6.726812024 + -0.5

Combine like terms: -6.726812024 + -0.5 = -7.226812024
x = -7.226812024

Simplifying
x = -7.226812024


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.226812024, -7.226812024}
Solution
x = {6.226812024, -7.226812024}

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