0=32+32x-16x^2

Solution for 0=32+32x-16x^2 equation:

Simplifying
0 = 32 + 32x + -16x2

Solving
0 = 32 + 32x + -16x2

Solving for variable 'x'.

Combine like terms: 0 + -32 = -32
-32 + -32x + 16x2 = 32 + 32x + -16x2 + -32 + -32x + 16x2

Reorder the terms:
-32 + -32x + 16x2 = 32 + -32 + 32x + -32x + -16x2 + 16x2

Combine like terms: 32 + -32 = 0
-32 + -32x + 16x2 = 0 + 32x + -32x + -16x2 + 16x2
-32 + -32x + 16x2 = 32x + -32x + -16x2 + 16x2

Combine like terms: 32x + -32x = 0
-32 + -32x + 16x2 = 0 + -16x2 + 16x2
-32 + -32x + 16x2 = -16x2 + 16x2

Combine like terms: -16x2 + 16x2 = 0
-32 + -32x + 16x2 = 0

Factor out the Greatest Common Factor (GCF), '16'.
16(-2 + -2x + x2) = 0

Ignore the factor 16.
Subproblem 1
Set the factor '(-2 + -2x + x2)' equal to zero and attempt to solve:

Simplifying
-2 + -2x + x2 = 0

Solving
-2 + -2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + -2x + 2 + x2 = 0 + 2

Reorder the terms:
-2 + 2 + -2x + x2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -2x + x2 = 0 + 2
-2x + x2 = 0 + 2

Combine like terms: 0 + 2 = 2
-2x + x2 = 2

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = 2 + 1

Reorder the terms:
1 + -2x + x2 = 2 + 1

Combine like terms: 2 + 1 = 3
1 + -2x + x2 = 3

Factor a perfect square on the left side:
(x + -1)(x + -1) = 3

Calculate the square root of the right side: 1.732050808

Break this problem into two subproblems by setting 
(x + -1) equal to 1.732050808 and -1.732050808.

Subproblem 1
x + -1 = 1.732050808

Simplifying
x + -1 = 1.732050808

Reorder the terms:
-1 + x = 1.732050808

Solving
-1 + x = 1.732050808

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = 1.732050808 + 1

Combine like terms: -1 + 1 = 0
0 + x = 1.732050808 + 1
x = 1.732050808 + 1

Combine like terms: 1.732050808 + 1 = 2.732050808
x = 2.732050808

Simplifying
x = 2.732050808

Subproblem 2
x + -1 = -1.732050808

Simplifying
x + -1 = -1.732050808

Reorder the terms:
-1 + x = -1.732050808

Solving
-1 + x = -1.732050808

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = -1.732050808 + 1

Combine like terms: -1 + 1 = 0
0 + x = -1.732050808 + 1
x = -1.732050808 + 1

Combine like terms: -1.732050808 + 1 = -0.732050808
x = -0.732050808

Simplifying
x = -0.732050808

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.732050808, -0.732050808}
Solution
x = {2.732050808, -0.732050808}