-.5*32x^2+39.2x=15.6

Solution for -.5*32x^2+39.2x=15.6 equation:

Simplifying
-0.5 * 32x2 + 39.2x = 15.6

Multiply -0.5 * 32
-16x2 + 39.2x = 15.6

Reorder the terms:
39.2x + -16x2 = 15.6

Solving
39.2x + -16x2 = 15.6

Solving for variable 'x'.

Reorder the terms:
-15.6 + 39.2x + -16x2 = 15.6 + -15.6

Combine like terms: 15.6 + -15.6 = 0.0
-15.6 + 39.2x + -16x2 = 0.0

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

Divide each side by '-16'.
0.975 + -2.45x + x2 = 0.0

Move the constant term to the right:

Add '-0.975' to each side of the equation.
0.975 + -2.45x + -0.975 + x2 = 0.0 + -0.975

Reorder the terms:
0.975 + -0.975 + -2.45x + x2 = 0.0 + -0.975

Combine like terms: 0.975 + -0.975 = 0.000
0.000 + -2.45x + x2 = 0.0 + -0.975
-2.45x + x2 = 0.0 + -0.975

Combine like terms: 0.0 + -0.975 = -0.975
-2.45x + x2 = -0.975

The x term is -2.45x.  Take half its coefficient (-1.225).
Square it (1.500625) and add it to both sides.

Add '1.500625' to each side of the equation.
-2.45x + 1.500625 + x2 = -0.975 + 1.500625

Reorder the terms:
1.500625 + -2.45x + x2 = -0.975 + 1.500625

Combine like terms: -0.975 + 1.500625 = 0.525625
1.500625 + -2.45x + x2 = 0.525625

Factor a perfect square on the left side:
(x + -1.225)(x + -1.225) = 0.525625

Calculate the square root of the right side: 0.725

Break this problem into two subproblems by setting 
(x + -1.225) equal to 0.725 and -0.725.

Subproblem 1
x + -1.225 = 0.725

Simplifying
x + -1.225 = 0.725

Reorder the terms:
-1.225 + x = 0.725

Solving
-1.225 + x = 0.725

Solving for variable 'x'.

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

Add '1.225' to each side of the equation.
-1.225 + 1.225 + x = 0.725 + 1.225

Combine like terms: -1.225 + 1.225 = 0.000
0.000 + x = 0.725 + 1.225
x = 0.725 + 1.225

Combine like terms: 0.725 + 1.225 = 1.95
x = 1.95

Simplifying
x = 1.95

Subproblem 2
x + -1.225 = -0.725

Simplifying
x + -1.225 = -0.725

Reorder the terms:
-1.225 + x = -0.725

Solving
-1.225 + x = -0.725

Solving for variable 'x'.

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

Add '1.225' to each side of the equation.
-1.225 + 1.225 + x = -0.725 + 1.225

Combine like terms: -1.225 + 1.225 = 0.000
0.000 + x = -0.725 + 1.225
x = -0.725 + 1.225

Combine like terms: -0.725 + 1.225 = 0.5
x = 0.5

Simplifying
x = 0.5

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.95, 0.5}