3200=8x+4x^2

Solution for 3200=8x+4x^2 equation:

Simplifying
3200 = 8x + 4x2

Solving
3200 = 8x + 4x2

Solving for variable 'x'.

Reorder the terms:
3200 + -8x + -4x2 = 8x + -8x + 4x2 + -4x2

Combine like terms: 8x + -8x = 0
3200 + -8x + -4x2 = 0 + 4x2 + -4x2
3200 + -8x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
3200 + -8x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(800 + -2x + -1x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(800 + -2x + -1x2)' equal to zero and attempt to solve:

Simplifying
800 + -2x + -1x2 = 0

Solving
800 + -2x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-800 + 2x + x2 = 0

Move the constant term to the right:

Add '800' to each side of the equation.
-800 + 2x + 800 + x2 = 0 + 800

Reorder the terms:
-800 + 800 + 2x + x2 = 0 + 800

Combine like terms: -800 + 800 = 0
0 + 2x + x2 = 0 + 800
2x + x2 = 0 + 800

Combine like terms: 0 + 800 = 800
2x + x2 = 800

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 = 800 + 1

Reorder the terms:
1 + 2x + x2 = 800 + 1

Combine like terms: 800 + 1 = 801
1 + 2x + x2 = 801

Factor a perfect square on the left side:
(x + 1)(x + 1) = 801

Calculate the square root of the right side: 28.301943396

Break this problem into two subproblems by setting 
(x + 1) equal to 28.301943396 and -28.301943396.

Subproblem 1
x + 1 = 28.301943396

Simplifying
x + 1 = 28.301943396

Reorder the terms:
1 + x = 28.301943396

Solving
1 + x = 28.301943396

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 = 28.301943396 + -1

Combine like terms: 1 + -1 = 0
0 + x = 28.301943396 + -1
x = 28.301943396 + -1

Combine like terms: 28.301943396 + -1 = 27.301943396
x = 27.301943396

Simplifying
x = 27.301943396

Subproblem 2
x + 1 = -28.301943396

Simplifying
x + 1 = -28.301943396

Reorder the terms:
1 + x = -28.301943396

Solving
1 + x = -28.301943396

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 = -28.301943396 + -1

Combine like terms: 1 + -1 = 0
0 + x = -28.301943396 + -1
x = -28.301943396 + -1

Combine like terms: -28.301943396 + -1 = -29.301943396
x = -29.301943396

Simplifying
x = -29.301943396

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {27.301943396, -29.301943396}
Solution
x = {27.301943396, -29.301943396}