4x^2+80x+108=0

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Solution for 4x^2+80x+108=0 equation: 


Simplifying
4x2 + 80x + 108 = 0

Reorder the terms:
108 + 80x + 4x2 = 0

Solving
108 + 80x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(27 + 20x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(27 + 20x + x2)' equal to zero and attempt to solve:

Simplifying
27 + 20x + x2 = 0

Solving
27 + 20x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-27' to each side of the equation.
27 + 20x + -27 + x2 = 0 + -27

Reorder the terms:
27 + -27 + 20x + x2 = 0 + -27

Combine like terms: 27 + -27 = 0
0 + 20x + x2 = 0 + -27
20x + x2 = 0 + -27

Combine like terms: 0 + -27 = -27
20x + x2 = -27

The x term is 20x.  Take half its coefficient (10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
20x + 100 + x2 = -27 + 100

Reorder the terms:
100 + 20x + x2 = -27 + 100

Combine like terms: -27 + 100 = 73
100 + 20x + x2 = 73

Factor a perfect square on the left side:
(x + 10)(x + 10) = 73

Calculate the square root of the right side: 8.544003745

Break this problem into two subproblems by setting 
(x + 10) equal to 8.544003745 and -8.544003745.


Subproblem 1
x + 10 = 8.544003745

Simplifying
x + 10 = 8.544003745

Reorder the terms:
10 + x = 8.544003745

Solving
10 + x = 8.544003745

Solving for variable 'x'.

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

Add '-10' to each side of the equation.
10 + -10 + x = 8.544003745 + -10

Combine like terms: 10 + -10 = 0
0 + x = 8.544003745 + -10
x = 8.544003745 + -10

Combine like terms: 8.544003745 + -10 = -1.455996255
x = -1.455996255

Simplifying
x = -1.455996255


Subproblem 2
x + 10 = -8.544003745

Simplifying
x + 10 = -8.544003745

Reorder the terms:
10 + x = -8.544003745

Solving
10 + x = -8.544003745

Solving for variable 'x'.

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

Add '-10' to each side of the equation.
10 + -10 + x = -8.544003745 + -10

Combine like terms: 10 + -10 = 0
0 + x = -8.544003745 + -10
x = -8.544003745 + -10

Combine like terms: -8.544003745 + -10 = -18.544003745
x = -18.544003745

Simplifying
x = -18.544003745


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.455996255, -18.544003745}
Solution
x = {-1.455996255, -18.544003745}

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