3632=-16x^2+514x+66

Solution for 3632=-16x^2+514x+66 equation:

Simplifying
3632 = -16x2 + 514x + 66

Reorder the terms:
3632 = 66 + 514x + -16x2

Solving
3632 = 66 + 514x + -16x2

Solving for variable 'x'.

Combine like terms: 3632 + -66 = 3566
3566 + -514x + 16x2 = 66 + 514x + -16x2 + -66 + -514x + 16x2

Reorder the terms:
3566 + -514x + 16x2 = 66 + -66 + 514x + -514x + -16x2 + 16x2

Combine like terms: 66 + -66 = 0
3566 + -514x + 16x2 = 0 + 514x + -514x + -16x2 + 16x2
3566 + -514x + 16x2 = 514x + -514x + -16x2 + 16x2

Combine like terms: 514x + -514x = 0
3566 + -514x + 16x2 = 0 + -16x2 + 16x2
3566 + -514x + 16x2 = -16x2 + 16x2

Combine like terms: -16x2 + 16x2 = 0
3566 + -514x + 16x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(1783 + -257x + 8x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(1783 + -257x + 8x2)' equal to zero and attempt to solve:

Simplifying
1783 + -257x + 8x2 = 0

Solving
1783 + -257x + 8x2 = 0

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

Divide each side by '8'.
222.875 + -32.125x + x2 = 0

Move the constant term to the right:

Add '-222.875' to each side of the equation.
222.875 + -32.125x + -222.875 + x2 = 0 + -222.875

Reorder the terms:
222.875 + -222.875 + -32.125x + x2 = 0 + -222.875

Combine like terms: 222.875 + -222.875 = 0.000
0.000 + -32.125x + x2 = 0 + -222.875
-32.125x + x2 = 0 + -222.875

Combine like terms: 0 + -222.875 = -222.875
-32.125x + x2 = -222.875

The x term is -32.125x.  Take half its coefficient (-16.0625).
Square it (258.0039063) and add it to both sides.

Add '258.0039063' to each side of the equation.
-32.125x + 258.0039063 + x2 = -222.875 + 258.0039063

Reorder the terms:
258.0039063 + -32.125x + x2 = -222.875 + 258.0039063

Combine like terms: -222.875 + 258.0039063 = 35.1289063
258.0039063 + -32.125x + x2 = 35.1289063

Factor a perfect square on the left side:
(x + -16.0625)(x + -16.0625) = 35.1289063

Calculate the square root of the right side: 5.926964341

Break this problem into two subproblems by setting 
(x + -16.0625) equal to 5.926964341 and -5.926964341.

Subproblem 1
x + -16.0625 = 5.926964341

Simplifying
x + -16.0625 = 5.926964341

Reorder the terms:
-16.0625 + x = 5.926964341

Solving
-16.0625 + x = 5.926964341

Solving for variable 'x'.

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

Add '16.0625' to each side of the equation.
-16.0625 + 16.0625 + x = 5.926964341 + 16.0625

Combine like terms: -16.0625 + 16.0625 = 0.0000
0.0000 + x = 5.926964341 + 16.0625
x = 5.926964341 + 16.0625

Combine like terms: 5.926964341 + 16.0625 = 21.989464341
x = 21.989464341

Simplifying
x = 21.989464341

Subproblem 2
x + -16.0625 = -5.926964341

Simplifying
x + -16.0625 = -5.926964341

Reorder the terms:
-16.0625 + x = -5.926964341

Solving
-16.0625 + x = -5.926964341

Solving for variable 'x'.

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

Add '16.0625' to each side of the equation.
-16.0625 + 16.0625 + x = -5.926964341 + 16.0625

Combine like terms: -16.0625 + 16.0625 = 0.0000
0.0000 + x = -5.926964341 + 16.0625
x = -5.926964341 + 16.0625

Combine like terms: -5.926964341 + 16.0625 = 10.135535659
x = 10.135535659

Simplifying
x = 10.135535659

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {21.989464341, 10.135535659}
Solution
x = {21.989464341, 10.135535659}