104.64=-.5*32x^2+40x+80

Solution for 104.64=-.5*32x^2+40x+80 equation:

Simplifying
104.64 = -0.5 * 32x2 + 40x + 80

Multiply -0.5 * 32
104.64 = -16x2 + 40x + 80

Reorder the terms:
104.64 = 80 + 40x + -16x2

Solving
104.64 = 80 + 40x + -16x2

Solving for variable 'x'.

Combine like terms: 104.64 + -80 = 24.64
24.64 + -40x + 16x2 = 80 + 40x + -16x2 + -80 + -40x + 16x2

Reorder the terms:
24.64 + -40x + 16x2 = 80 + -80 + 40x + -40x + -16x2 + 16x2

Combine like terms: 80 + -80 = 0
24.64 + -40x + 16x2 = 0 + 40x + -40x + -16x2 + 16x2
24.64 + -40x + 16x2 = 40x + -40x + -16x2 + 16x2

Combine like terms: 40x + -40x = 0
24.64 + -40x + 16x2 = 0 + -16x2 + 16x2
24.64 + -40x + 16x2 = -16x2 + 16x2

Combine like terms: -16x2 + 16x2 = 0
24.64 + -40x + 16x2 = 0

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

Divide each side by '16'.
1.54 + -2.5x + x2 = 0

Move the constant term to the right:

Add '-1.54' to each side of the equation.
1.54 + -2.5x + -1.54 + x2 = 0 + -1.54

Reorder the terms:
1.54 + -1.54 + -2.5x + x2 = 0 + -1.54

Combine like terms: 1.54 + -1.54 = 0.00
0.00 + -2.5x + x2 = 0 + -1.54
-2.5x + x2 = 0 + -1.54

Combine like terms: 0 + -1.54 = -1.54
-2.5x + x2 = -1.54

The x term is -2.5x.  Take half its coefficient (-1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
-2.5x + 1.5625 + x2 = -1.54 + 1.5625

Reorder the terms:
1.5625 + -2.5x + x2 = -1.54 + 1.5625

Combine like terms: -1.54 + 1.5625 = 0.0225
1.5625 + -2.5x + x2 = 0.0225

Factor a perfect square on the left side:
(x + -1.25)(x + -1.25) = 0.0225

Calculate the square root of the right side: 0.15

Break this problem into two subproblems by setting 
(x + -1.25) equal to 0.15 and -0.15.

Subproblem 1
x + -1.25 = 0.15

Simplifying
x + -1.25 = 0.15

Reorder the terms:
-1.25 + x = 0.15

Solving
-1.25 + x = 0.15

Solving for variable 'x'.

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

Add '1.25' to each side of the equation.
-1.25 + 1.25 + x = 0.15 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + x = 0.15 + 1.25
x = 0.15 + 1.25

Combine like terms: 0.15 + 1.25 = 1.4
x = 1.4

Simplifying
x = 1.4

Subproblem 2
x + -1.25 = -0.15

Simplifying
x + -1.25 = -0.15

Reorder the terms:
-1.25 + x = -0.15

Solving
-1.25 + x = -0.15

Solving for variable 'x'.

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

Add '1.25' to each side of the equation.
-1.25 + 1.25 + x = -0.15 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + x = -0.15 + 1.25
x = -0.15 + 1.25

Combine like terms: -0.15 + 1.25 = 1.1
x = 1.1

Simplifying
x = 1.1

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.4, 1.1}