4x^2+88x+180=0

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Solution for 4x^2+88x+180=0 equation: 


Simplifying
4x2 + 88x + 180 = 0

Reorder the terms:
180 + 88x + 4x2 = 0

Solving
180 + 88x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(45 + 22x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(45 + 22x + x2)' equal to zero and attempt to solve:

Simplifying
45 + 22x + x2 = 0

Solving
45 + 22x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-45' to each side of the equation.
45 + 22x + -45 + x2 = 0 + -45

Reorder the terms:
45 + -45 + 22x + x2 = 0 + -45

Combine like terms: 45 + -45 = 0
0 + 22x + x2 = 0 + -45
22x + x2 = 0 + -45

Combine like terms: 0 + -45 = -45
22x + x2 = -45

The x term is 22x.  Take half its coefficient (11).
Square it (121) and add it to both sides.

Add '121' to each side of the equation.
22x + 121 + x2 = -45 + 121

Reorder the terms:
121 + 22x + x2 = -45 + 121

Combine like terms: -45 + 121 = 76
121 + 22x + x2 = 76

Factor a perfect square on the left side:
(x + 11)(x + 11) = 76

Calculate the square root of the right side: 8.717797887

Break this problem into two subproblems by setting 
(x + 11) equal to 8.717797887 and -8.717797887.


Subproblem 1
x + 11 = 8.717797887

Simplifying
x + 11 = 8.717797887

Reorder the terms:
11 + x = 8.717797887

Solving
11 + x = 8.717797887

Solving for variable 'x'.

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

Add '-11' to each side of the equation.
11 + -11 + x = 8.717797887 + -11

Combine like terms: 11 + -11 = 0
0 + x = 8.717797887 + -11
x = 8.717797887 + -11

Combine like terms: 8.717797887 + -11 = -2.282202113
x = -2.282202113

Simplifying
x = -2.282202113


Subproblem 2
x + 11 = -8.717797887

Simplifying
x + 11 = -8.717797887

Reorder the terms:
11 + x = -8.717797887

Solving
11 + x = -8.717797887

Solving for variable 'x'.

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

Add '-11' to each side of the equation.
11 + -11 + x = -8.717797887 + -11

Combine like terms: 11 + -11 = 0
0 + x = -8.717797887 + -11
x = -8.717797887 + -11

Combine like terms: -8.717797887 + -11 = -19.717797887
x = -19.717797887

Simplifying
x = -19.717797887


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-2.282202113, -19.717797887}
Solution
x = {-2.282202113, -19.717797887}

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