4x^2+40x-96=80

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Solution for 4x^2+40x-96=80 equation: 


Simplifying
4x2 + 40x + -96 = 80

Reorder the terms:
-96 + 40x + 4x2 = 80

Solving
-96 + 40x + 4x2 = 80

Solving for variable 'x'.

Reorder the terms:
-96 + -80 + 40x + 4x2 = 80 + -80

Combine like terms: -96 + -80 = -176
-176 + 40x + 4x2 = 80 + -80

Combine like terms: 80 + -80 = 0
-176 + 40x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-44 + 10x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-44 + 10x + x2)' equal to zero and attempt to solve:

Simplifying
-44 + 10x + x2 = 0

Solving
-44 + 10x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '44' to each side of the equation.
-44 + 10x + 44 + x2 = 0 + 44

Reorder the terms:
-44 + 44 + 10x + x2 = 0 + 44

Combine like terms: -44 + 44 = 0
0 + 10x + x2 = 0 + 44
10x + x2 = 0 + 44

Combine like terms: 0 + 44 = 44
10x + x2 = 44

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 = 44 + 25

Reorder the terms:
25 + 10x + x2 = 44 + 25

Combine like terms: 44 + 25 = 69
25 + 10x + x2 = 69

Factor a perfect square on the left side:
(x + 5)(x + 5) = 69

Calculate the square root of the right side: 8.306623863

Break this problem into two subproblems by setting 
(x + 5) equal to 8.306623863 and -8.306623863.


Subproblem 1
x + 5 = 8.306623863

Simplifying
x + 5 = 8.306623863

Reorder the terms:
5 + x = 8.306623863

Solving
5 + x = 8.306623863

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 = 8.306623863 + -5

Combine like terms: 5 + -5 = 0
0 + x = 8.306623863 + -5
x = 8.306623863 + -5

Combine like terms: 8.306623863 + -5 = 3.306623863
x = 3.306623863

Simplifying
x = 3.306623863


Subproblem 2
x + 5 = -8.306623863

Simplifying
x + 5 = -8.306623863

Reorder the terms:
5 + x = -8.306623863

Solving
5 + x = -8.306623863

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 = -8.306623863 + -5

Combine like terms: 5 + -5 = 0
0 + x = -8.306623863 + -5
x = -8.306623863 + -5

Combine like terms: -8.306623863 + -5 = -13.306623863
x = -13.306623863

Simplifying
x = -13.306623863


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.306623863, -13.306623863}
Solution
x = {3.306623863, -13.306623863}

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