4x^2+40x-92=0

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Solution for 4x^2+40x-92=0 equation: 


Simplifying
4x2 + 40x + -92 = 0

Reorder the terms:
-92 + 40x + 4x2 = 0

Solving
-92 + 40x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-23 + 10x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-23 + 10x + x2)' equal to zero and attempt to solve:

Simplifying
-23 + 10x + x2 = 0

Solving
-23 + 10x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '23' to each side of the equation.
-23 + 10x + 23 + x2 = 0 + 23

Reorder the terms:
-23 + 23 + 10x + x2 = 0 + 23

Combine like terms: -23 + 23 = 0
0 + 10x + x2 = 0 + 23
10x + x2 = 0 + 23

Combine like terms: 0 + 23 = 23
10x + x2 = 23

The x term is 10x.  Take half its coefficient (5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
10x + 25 + x2 = 23 + 25

Reorder the terms:
25 + 10x + x2 = 23 + 25

Combine like terms: 23 + 25 = 48
25 + 10x + x2 = 48

Factor a perfect square on the left side:
(x + 5)(x + 5) = 48

Calculate the square root of the right side: 6.92820323

Break this problem into two subproblems by setting 
(x + 5) equal to 6.92820323 and -6.92820323.


Subproblem 1
x + 5 = 6.92820323

Simplifying
x + 5 = 6.92820323

Reorder the terms:
5 + x = 6.92820323

Solving
5 + x = 6.92820323

Solving for variable 'x'.

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

Add '-5' to each side of the equation.
5 + -5 + x = 6.92820323 + -5

Combine like terms: 5 + -5 = 0
0 + x = 6.92820323 + -5
x = 6.92820323 + -5

Combine like terms: 6.92820323 + -5 = 1.92820323
x = 1.92820323

Simplifying
x = 1.92820323


Subproblem 2
x + 5 = -6.92820323

Simplifying
x + 5 = -6.92820323

Reorder the terms:
5 + x = -6.92820323

Solving
5 + x = -6.92820323

Solving for variable 'x'.

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

Add '-5' to each side of the equation.
5 + -5 + x = -6.92820323 + -5

Combine like terms: 5 + -5 = 0
0 + x = -6.92820323 + -5
x = -6.92820323 + -5

Combine like terms: -6.92820323 + -5 = -11.92820323
x = -11.92820323

Simplifying
x = -11.92820323


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.92820323, -11.92820323}
Solution
x = {1.92820323, -11.92820323}

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