4x^2+92x-56=0

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Solution for 4x^2+92x-56=0 equation: 


Simplifying
4x2 + 92x + -56 = 0

Reorder the terms:
-56 + 92x + 4x2 = 0

Solving
-56 + 92x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-14 + 23x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-14 + 23x + x2)' equal to zero and attempt to solve:

Simplifying
-14 + 23x + x2 = 0

Solving
-14 + 23x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '14' to each side of the equation.
-14 + 23x + 14 + x2 = 0 + 14

Reorder the terms:
-14 + 14 + 23x + x2 = 0 + 14

Combine like terms: -14 + 14 = 0
0 + 23x + x2 = 0 + 14
23x + x2 = 0 + 14

Combine like terms: 0 + 14 = 14
23x + x2 = 14

The x term is 23x.  Take half its coefficient (11.5).
Square it (132.25) and add it to both sides.

Add '132.25' to each side of the equation.
23x + 132.25 + x2 = 14 + 132.25

Reorder the terms:
132.25 + 23x + x2 = 14 + 132.25

Combine like terms: 14 + 132.25 = 146.25
132.25 + 23x + x2 = 146.25

Factor a perfect square on the left side:
(x + 11.5)(x + 11.5) = 146.25

Calculate the square root of the right side: 12.093386622

Break this problem into two subproblems by setting 
(x + 11.5) equal to 12.093386622 and -12.093386622.


Subproblem 1
x + 11.5 = 12.093386622

Simplifying
x + 11.5 = 12.093386622

Reorder the terms:
11.5 + x = 12.093386622

Solving
11.5 + x = 12.093386622

Solving for variable 'x'.

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

Add '-11.5' to each side of the equation.
11.5 + -11.5 + x = 12.093386622 + -11.5

Combine like terms: 11.5 + -11.5 = 0.0
0.0 + x = 12.093386622 + -11.5
x = 12.093386622 + -11.5

Combine like terms: 12.093386622 + -11.5 = 0.593386622
x = 0.593386622

Simplifying
x = 0.593386622


Subproblem 2
x + 11.5 = -12.093386622

Simplifying
x + 11.5 = -12.093386622

Reorder the terms:
11.5 + x = -12.093386622

Solving
11.5 + x = -12.093386622

Solving for variable 'x'.

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

Add '-11.5' to each side of the equation.
11.5 + -11.5 + x = -12.093386622 + -11.5

Combine like terms: 11.5 + -11.5 = 0.0
0.0 + x = -12.093386622 + -11.5
x = -12.093386622 + -11.5

Combine like terms: -12.093386622 + -11.5 = -23.593386622
x = -23.593386622

Simplifying
x = -23.593386622


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.593386622, -23.593386622}
Solution
x = {0.593386622, -23.593386622}

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