16x^2-80x-3=0

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Solution for 16x^2-80x-3=0 equation: 


Simplifying
16x2 + -80x + -3 = 0

Reorder the terms:
-3 + -80x + 16x2 = 0

Solving
-3 + -80x + 16x2 = 0

Solving for variable 'x'.

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

Divide each side by '16'.
-0.1875 + -5x + x2 = 0

Move the constant term to the right:

Add '0.1875' to each side of the equation.
-0.1875 + -5x + 0.1875 + x2 = 0 + 0.1875

Reorder the terms:
-0.1875 + 0.1875 + -5x + x2 = 0 + 0.1875

Combine like terms: -0.1875 + 0.1875 = 0.0000
0.0000 + -5x + x2 = 0 + 0.1875
-5x + x2 = 0 + 0.1875

Combine like terms: 0 + 0.1875 = 0.1875
-5x + x2 = 0.1875

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 = 0.1875 + 6.25

Reorder the terms:
6.25 + -5x + x2 = 0.1875 + 6.25

Combine like terms: 0.1875 + 6.25 = 6.4375
6.25 + -5x + x2 = 6.4375

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 6.4375

Calculate the square root of the right side: 2.537222891

Break this problem into two subproblems by setting 
(x + -2.5) equal to 2.537222891 and -2.537222891.


Subproblem 1
x + -2.5 = 2.537222891

Simplifying
x + -2.5 = 2.537222891

Reorder the terms:
-2.5 + x = 2.537222891

Solving
-2.5 + x = 2.537222891

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 = 2.537222891 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = 2.537222891 + 2.5
x = 2.537222891 + 2.5

Combine like terms: 2.537222891 + 2.5 = 5.037222891
x = 5.037222891

Simplifying
x = 5.037222891


Subproblem 2
x + -2.5 = -2.537222891

Simplifying
x + -2.5 = -2.537222891

Reorder the terms:
-2.5 + x = -2.537222891

Solving
-2.5 + x = -2.537222891

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 = -2.537222891 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = -2.537222891 + 2.5
x = -2.537222891 + 2.5

Combine like terms: -2.537222891 + 2.5 = -0.037222891
x = -0.037222891

Simplifying
x = -0.037222891


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.037222891, -0.037222891}

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