80(x)=80-16x^2

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Solution for 80(x)=80-16x^2 equation: 


Simplifying
80(x) = 80 + -16x2

Solving
80x = 80 + -16x2

Solving for variable 'x'.

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

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

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

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

Factor out the Greatest Common Factor (GCF), '16'.
16(-5 + 5x + x2) = 0

Ignore the factor 16.

Subproblem 1
Set the factor '(-5 + 5x + x2)' equal to zero and attempt to solve:

Simplifying
-5 + 5x + x2 = 0

Solving
-5 + 5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

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

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

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

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

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 = 5 + 6.25

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

Combine like terms: 5 + 6.25 = 11.25
6.25 + 5x + x2 = 11.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 11.25

Calculate the square root of the right side: 3.354101966

Break this problem into two subproblems by setting 
(x + 2.5) equal to 3.354101966 and -3.354101966.


Subproblem 1
x + 2.5 = 3.354101966

Simplifying
x + 2.5 = 3.354101966

Reorder the terms:
2.5 + x = 3.354101966

Solving
2.5 + x = 3.354101966

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 = 3.354101966 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 3.354101966 + -2.5
x = 3.354101966 + -2.5

Combine like terms: 3.354101966 + -2.5 = 0.854101966
x = 0.854101966

Simplifying
x = 0.854101966


Subproblem 2
x + 2.5 = -3.354101966

Simplifying
x + 2.5 = -3.354101966

Reorder the terms:
2.5 + x = -3.354101966

Solving
2.5 + x = -3.354101966

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 = -3.354101966 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -3.354101966 + -2.5
x = -3.354101966 + -2.5

Combine like terms: -3.354101966 + -2.5 = -5.854101966
x = -5.854101966

Simplifying
x = -5.854101966


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.854101966, -5.854101966}
Solution
x = {0.854101966, -5.854101966}

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