80x-4x*4x=76

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Solution for 80x-4x*4x=76 equation: 


Simplifying
80x + -4x * 4x = 76

Reorder the terms for easier multiplication:
80x + -4 * 4x * x = 76

Multiply -4 * 4
80x + -16x * x = 76

Multiply x * x
80x + -16x2 = 76

Solving
80x + -16x2 = 76

Solving for variable 'x'.

Reorder the terms:
-76 + 80x + -16x2 = 76 + -76

Combine like terms: 76 + -76 = 0
-76 + 80x + -16x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-19 + 20x + -4x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-19 + 20x + -4x2)' equal to zero and attempt to solve:

Simplifying
-19 + 20x + -4x2 = 0

Solving
-19 + 20x + -4x2 = 0

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
4.75 + -5x + x2 = 0

Move the constant term to the right:

Add '-4.75' to each side of the equation.
4.75 + -5x + -4.75 + x2 = 0 + -4.75

Reorder the terms:
4.75 + -4.75 + -5x + x2 = 0 + -4.75

Combine like terms: 4.75 + -4.75 = 0.00
0.00 + -5x + x2 = 0 + -4.75
-5x + x2 = 0 + -4.75

Combine like terms: 0 + -4.75 = -4.75
-5x + x2 = -4.75

The x term is -5x.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5x + 6.25 + x2 = -4.75 + 6.25

Reorder the terms:
6.25 + -5x + x2 = -4.75 + 6.25

Combine like terms: -4.75 + 6.25 = 1.5
6.25 + -5x + x2 = 1.5

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 1.5

Calculate the square root of the right side: 1.224744871

Break this problem into two subproblems by setting 
(x + -2.5) equal to 1.224744871 and -1.224744871.


Subproblem 1
x + -2.5 = 1.224744871

Simplifying
x + -2.5 = 1.224744871

Reorder the terms:
-2.5 + x = 1.224744871

Solving
-2.5 + x = 1.224744871

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = 1.224744871 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = 1.224744871 + 2.5
x = 1.224744871 + 2.5

Combine like terms: 1.224744871 + 2.5 = 3.724744871
x = 3.724744871

Simplifying
x = 3.724744871


Subproblem 2
x + -2.5 = -1.224744871

Simplifying
x + -2.5 = -1.224744871

Reorder the terms:
-2.5 + x = -1.224744871

Solving
-2.5 + x = -1.224744871

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = -1.224744871 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = -1.224744871 + 2.5
x = -1.224744871 + 2.5

Combine like terms: -1.224744871 + 2.5 = 1.275255129
x = 1.275255129

Simplifying
x = 1.275255129


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.724744871, 1.275255129}
Solution
x = {3.724744871, 1.275255129}

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