(-16)x^2+80x+4=0

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Solution for (-16)x^2+80x+4=0 equation: 


Simplifying
(-16) * x2 + 80x + 4 = 0

Reorder the terms:
4 + 80x + -16x2 = 0

Solving
4 + 80x + -16x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(1 + 20x + -4x2) = 0

Ignore the factor 4.

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

Simplifying
1 + 20x + -4x2 = 0

Solving
1 + 20x + -4x2 = 0

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

Divide each side by '-4'.
-0.25 + -5x + x2 = 0

Move the constant term to the right:

Add '0.25' to each side of the equation.
-0.25 + -5x + 0.25 + x2 = 0 + 0.25

Reorder the terms:
-0.25 + 0.25 + -5x + x2 = 0 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + -5x + x2 = 0 + 0.25
-5x + x2 = 0 + 0.25

Combine like terms: 0 + 0.25 = 0.25
-5x + x2 = 0.25

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 = 0.25 + 6.25

Reorder the terms:
6.25 + -5x + x2 = 0.25 + 6.25

Combine like terms: 0.25 + 6.25 = 6.5
6.25 + -5x + x2 = 6.5

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 6.5

Calculate the square root of the right side: 2.549509757

Break this problem into two subproblems by setting 
(x + -2.5) equal to 2.549509757 and -2.549509757.


Subproblem 1
x + -2.5 = 2.549509757

Simplifying
x + -2.5 = 2.549509757

Reorder the terms:
-2.5 + x = 2.549509757

Solving
-2.5 + x = 2.549509757

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 = 2.549509757 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = 2.549509757 + 2.5
x = 2.549509757 + 2.5

Combine like terms: 2.549509757 + 2.5 = 5.049509757
x = 5.049509757

Simplifying
x = 5.049509757


Subproblem 2
x + -2.5 = -2.549509757

Simplifying
x + -2.5 = -2.549509757

Reorder the terms:
-2.5 + x = -2.549509757

Solving
-2.5 + x = -2.549509757

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 = -2.549509757 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = -2.549509757 + 2.5
x = -2.549509757 + 2.5

Combine like terms: -2.549509757 + 2.5 = -0.049509757
x = -0.049509757

Simplifying
x = -0.049509757


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.049509757, -0.049509757}
Solution
x = {5.049509757, -0.049509757}

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