16=33x-16x^2

Solution for 16=33x-16x^2 equation:

Simplifying
16 = 33x + -16x2

Solving
16 = 33x + -16x2

Solving for variable 'x'.

Reorder the terms:
16 + -33x + 16x2 = 33x + -33x + -16x2 + 16x2

Combine like terms: 33x + -33x = 0
16 + -33x + 16x2 = 0 + -16x2 + 16x2
16 + -33x + 16x2 = -16x2 + 16x2

Combine like terms: -16x2 + 16x2 = 0
16 + -33x + 16x2 = 0

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

Divide each side by '16'.
1 + -2.0625x + x2 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + -2.0625x + -1 + x2 = 0 + -1

Reorder the terms:
1 + -1 + -2.0625x + x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2.0625x + x2 = 0 + -1
-2.0625x + x2 = 0 + -1

Combine like terms: 0 + -1 = -1
-2.0625x + x2 = -1

The x term is -2.0625x.  Take half its coefficient (-1.03125).
Square it (1.063476563) and add it to both sides.

Add '1.063476563' to each side of the equation.
-2.0625x + 1.063476563 + x2 = -1 + 1.063476563

Reorder the terms:
1.063476563 + -2.0625x + x2 = -1 + 1.063476563

Combine like terms: -1 + 1.063476563 = 0.063476563
1.063476563 + -2.0625x + x2 = 0.063476563

Factor a perfect square on the left side:
(x + -1.03125)(x + -1.03125) = 0.063476563

Calculate the square root of the right side: 0.251945556

Break this problem into two subproblems by setting 
(x + -1.03125) equal to 0.251945556 and -0.251945556.

Subproblem 1
x + -1.03125 = 0.251945556

Simplifying
x + -1.03125 = 0.251945556

Reorder the terms:
-1.03125 + x = 0.251945556

Solving
-1.03125 + x = 0.251945556

Solving for variable 'x'.

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

Add '1.03125' to each side of the equation.
-1.03125 + 1.03125 + x = 0.251945556 + 1.03125

Combine like terms: -1.03125 + 1.03125 = 0.00000
0.00000 + x = 0.251945556 + 1.03125
x = 0.251945556 + 1.03125

Combine like terms: 0.251945556 + 1.03125 = 1.283195556
x = 1.283195556

Simplifying
x = 1.283195556

Subproblem 2
x + -1.03125 = -0.251945556

Simplifying
x + -1.03125 = -0.251945556

Reorder the terms:
-1.03125 + x = -0.251945556

Solving
-1.03125 + x = -0.251945556

Solving for variable 'x'.

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

Add '1.03125' to each side of the equation.
-1.03125 + 1.03125 + x = -0.251945556 + 1.03125

Combine like terms: -1.03125 + 1.03125 = 0.00000
0.00000 + x = -0.251945556 + 1.03125
x = -0.251945556 + 1.03125

Combine like terms: -0.251945556 + 1.03125 = 0.779304444
x = 0.779304444

Simplifying
x = 0.779304444

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.283195556, 0.779304444}