4x^2+36x-92=0

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Solution for 4x^2+36x-92=0 equation: 


Simplifying
4x2 + 36x + -92 = 0

Reorder the terms:
-92 + 36x + 4x2 = 0

Solving
-92 + 36x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-23 + 9x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-23 + 9x + x2)' equal to zero and attempt to solve:

Simplifying
-23 + 9x + x2 = 0

Solving
-23 + 9x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '23' to each side of the equation.
-23 + 9x + 23 + x2 = 0 + 23

Reorder the terms:
-23 + 23 + 9x + x2 = 0 + 23

Combine like terms: -23 + 23 = 0
0 + 9x + x2 = 0 + 23
9x + x2 = 0 + 23

Combine like terms: 0 + 23 = 23
9x + x2 = 23

The x term is 9x.  Take half its coefficient (4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
9x + 20.25 + x2 = 23 + 20.25

Reorder the terms:
20.25 + 9x + x2 = 23 + 20.25

Combine like terms: 23 + 20.25 = 43.25
20.25 + 9x + x2 = 43.25

Factor a perfect square on the left side:
(x + 4.5)(x + 4.5) = 43.25

Calculate the square root of the right side: 6.576473219

Break this problem into two subproblems by setting 
(x + 4.5) equal to 6.576473219 and -6.576473219.


Subproblem 1
x + 4.5 = 6.576473219

Simplifying
x + 4.5 = 6.576473219

Reorder the terms:
4.5 + x = 6.576473219

Solving
4.5 + x = 6.576473219

Solving for variable 'x'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + x = 6.576473219 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + x = 6.576473219 + -4.5
x = 6.576473219 + -4.5

Combine like terms: 6.576473219 + -4.5 = 2.076473219
x = 2.076473219

Simplifying
x = 2.076473219


Subproblem 2
x + 4.5 = -6.576473219

Simplifying
x + 4.5 = -6.576473219

Reorder the terms:
4.5 + x = -6.576473219

Solving
4.5 + x = -6.576473219

Solving for variable 'x'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + x = -6.576473219 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + x = -6.576473219 + -4.5
x = -6.576473219 + -4.5

Combine like terms: -6.576473219 + -4.5 = -11.076473219
x = -11.076473219

Simplifying
x = -11.076473219


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.076473219, -11.076473219}
Solution
x = {2.076473219, -11.076473219}

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