-16x^2+80x+4.5=0

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Solution for -16x^2+80x+4.5=0 equation: 


Simplifying
-16x2 + 80x + 4.5 = 0

Reorder the terms:
4.5 + 80x + -16x2 = 0

Solving
4.5 + 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'.
-0.28125 + -5x + x2 = 0

Move the constant term to the right:

Add '0.28125' to each side of the equation.
-0.28125 + -5x + 0.28125 + x2 = 0 + 0.28125

Reorder the terms:
-0.28125 + 0.28125 + -5x + x2 = 0 + 0.28125

Combine like terms: -0.28125 + 0.28125 = 0.00000
0.00000 + -5x + x2 = 0 + 0.28125
-5x + x2 = 0 + 0.28125

Combine like terms: 0 + 0.28125 = 0.28125
-5x + x2 = 0.28125

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 = 0.28125 + 6.25

Reorder the terms:
6.25 + -5x + x2 = 0.28125 + 6.25

Combine like terms: 0.28125 + 6.25 = 6.53125
6.25 + -5x + x2 = 6.53125

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 6.53125

Calculate the square root of the right side: 2.555631038

Break this problem into two subproblems by setting 
(x + -2.5) equal to 2.555631038 and -2.555631038.


Subproblem 1
x + -2.5 = 2.555631038

Simplifying
x + -2.5 = 2.555631038

Reorder the terms:
-2.5 + x = 2.555631038

Solving
-2.5 + x = 2.555631038

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 = 2.555631038 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = 2.555631038 + 2.5
x = 2.555631038 + 2.5

Combine like terms: 2.555631038 + 2.5 = 5.055631038
x = 5.055631038

Simplifying
x = 5.055631038


Subproblem 2
x + -2.5 = -2.555631038

Simplifying
x + -2.5 = -2.555631038

Reorder the terms:
-2.5 + x = -2.555631038

Solving
-2.5 + x = -2.555631038

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 = -2.555631038 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = -2.555631038 + 2.5
x = -2.555631038 + 2.5

Combine like terms: -2.555631038 + 2.5 = -0.055631038
x = -0.055631038

Simplifying
x = -0.055631038


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.055631038, -0.055631038}

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