4x^2+58x-108=0

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Solution for 4x^2+58x-108=0 equation: 


Simplifying
4x2 + 58x + -108 = 0

Reorder the terms:
-108 + 58x + 4x2 = 0

Solving
-108 + 58x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-54 + 29x + 2x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-54 + 29x + 2x2)' equal to zero and attempt to solve:

Simplifying
-54 + 29x + 2x2 = 0

Solving
-54 + 29x + 2x2 = 0

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

Divide each side by '2'.
-27 + 14.5x + x2 = 0

Move the constant term to the right:

Add '27' to each side of the equation.
-27 + 14.5x + 27 + x2 = 0 + 27

Reorder the terms:
-27 + 27 + 14.5x + x2 = 0 + 27

Combine like terms: -27 + 27 = 0
0 + 14.5x + x2 = 0 + 27
14.5x + x2 = 0 + 27

Combine like terms: 0 + 27 = 27
14.5x + x2 = 27

The x term is 14.5x.  Take half its coefficient (7.25).
Square it (52.5625) and add it to both sides.

Add '52.5625' to each side of the equation.
14.5x + 52.5625 + x2 = 27 + 52.5625

Reorder the terms:
52.5625 + 14.5x + x2 = 27 + 52.5625

Combine like terms: 27 + 52.5625 = 79.5625
52.5625 + 14.5x + x2 = 79.5625

Factor a perfect square on the left side:
(x + 7.25)(x + 7.25) = 79.5625

Calculate the square root of the right side: 8.919781387

Break this problem into two subproblems by setting 
(x + 7.25) equal to 8.919781387 and -8.919781387.


Subproblem 1
x + 7.25 = 8.919781387

Simplifying
x + 7.25 = 8.919781387

Reorder the terms:
7.25 + x = 8.919781387

Solving
7.25 + x = 8.919781387

Solving for variable 'x'.

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

Add '-7.25' to each side of the equation.
7.25 + -7.25 + x = 8.919781387 + -7.25

Combine like terms: 7.25 + -7.25 = 0.00
0.00 + x = 8.919781387 + -7.25
x = 8.919781387 + -7.25

Combine like terms: 8.919781387 + -7.25 = 1.669781387
x = 1.669781387

Simplifying
x = 1.669781387


Subproblem 2
x + 7.25 = -8.919781387

Simplifying
x + 7.25 = -8.919781387

Reorder the terms:
7.25 + x = -8.919781387

Solving
7.25 + x = -8.919781387

Solving for variable 'x'.

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

Add '-7.25' to each side of the equation.
7.25 + -7.25 + x = -8.919781387 + -7.25

Combine like terms: 7.25 + -7.25 = 0.00
0.00 + x = -8.919781387 + -7.25
x = -8.919781387 + -7.25

Combine like terms: -8.919781387 + -7.25 = -16.169781387
x = -16.169781387

Simplifying
x = -16.169781387


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.669781387, -16.169781387}
Solution
x = {1.669781387, -16.169781387}

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