4x^2-32x-180=0

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Solution for 4x^2-32x-180=0 equation: 


Simplifying
4x2 + -32x + -180 = 0

Reorder the terms:
-180 + -32x + 4x2 = 0

Solving
-180 + -32x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-45 + -8x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-45 + -8x + x2)' equal to zero and attempt to solve:

Simplifying
-45 + -8x + x2 = 0

Solving
-45 + -8x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '45' to each side of the equation.
-45 + -8x + 45 + x2 = 0 + 45

Reorder the terms:
-45 + 45 + -8x + x2 = 0 + 45

Combine like terms: -45 + 45 = 0
0 + -8x + x2 = 0 + 45
-8x + x2 = 0 + 45

Combine like terms: 0 + 45 = 45
-8x + x2 = 45

The x term is -8x.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8x + 16 + x2 = 45 + 16

Reorder the terms:
16 + -8x + x2 = 45 + 16

Combine like terms: 45 + 16 = 61
16 + -8x + x2 = 61

Factor a perfect square on the left side:
(x + -4)(x + -4) = 61

Calculate the square root of the right side: 7.810249676

Break this problem into two subproblems by setting 
(x + -4) equal to 7.810249676 and -7.810249676.


Subproblem 1
x + -4 = 7.810249676

Simplifying
x + -4 = 7.810249676

Reorder the terms:
-4 + x = 7.810249676

Solving
-4 + x = 7.810249676

Solving for variable 'x'.

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

Add '4' to each side of the equation.
-4 + 4 + x = 7.810249676 + 4

Combine like terms: -4 + 4 = 0
0 + x = 7.810249676 + 4
x = 7.810249676 + 4

Combine like terms: 7.810249676 + 4 = 11.810249676
x = 11.810249676

Simplifying
x = 11.810249676


Subproblem 2
x + -4 = -7.810249676

Simplifying
x + -4 = -7.810249676

Reorder the terms:
-4 + x = -7.810249676

Solving
-4 + x = -7.810249676

Solving for variable 'x'.

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

Add '4' to each side of the equation.
-4 + 4 + x = -7.810249676 + 4

Combine like terms: -4 + 4 = 0
0 + x = -7.810249676 + 4
x = -7.810249676 + 4

Combine like terms: -7.810249676 + 4 = -3.810249676
x = -3.810249676

Simplifying
x = -3.810249676


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {11.810249676, -3.810249676}
Solution
x = {11.810249676, -3.810249676}

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