500=4+x(650-10x)

Solution for 500=4+x(650-10x) equation:

Simplifying
500 = 4 + x(650 + -10x)
500 = 4 + (650 * x + -10x * x)
500 = 4 + (650x + -10x2)

Solving
500 = 4 + 650x + -10x2

Solving for variable 'x'.

Combine like terms: 500 + -4 = 496
496 + -650x + 10x2 = 4 + 650x + -10x2 + -4 + -650x + 10x2

Reorder the terms:
496 + -650x + 10x2 = 4 + -4 + 650x + -650x + -10x2 + 10x2

Combine like terms: 4 + -4 = 0
496 + -650x + 10x2 = 0 + 650x + -650x + -10x2 + 10x2
496 + -650x + 10x2 = 650x + -650x + -10x2 + 10x2

Combine like terms: 650x + -650x = 0
496 + -650x + 10x2 = 0 + -10x2 + 10x2
496 + -650x + 10x2 = -10x2 + 10x2

Combine like terms: -10x2 + 10x2 = 0
496 + -650x + 10x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(248 + -325x + 5x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(248 + -325x + 5x2)' equal to zero and attempt to solve:

Simplifying
248 + -325x + 5x2 = 0

Solving
248 + -325x + 5x2 = 0

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

Divide each side by '5'.
49.6 + -65x + x2 = 0

Move the constant term to the right:

Add '-49.6' to each side of the equation.
49.6 + -65x + -49.6 + x2 = 0 + -49.6

Reorder the terms:
49.6 + -49.6 + -65x + x2 = 0 + -49.6

Combine like terms: 49.6 + -49.6 = 0.0
0.0 + -65x + x2 = 0 + -49.6
-65x + x2 = 0 + -49.6

Combine like terms: 0 + -49.6 = -49.6
-65x + x2 = -49.6

The x term is -65x.  Take half its coefficient (-32.5).
Square it (1056.25) and add it to both sides.

Add '1056.25' to each side of the equation.
-65x + 1056.25 + x2 = -49.6 + 1056.25

Reorder the terms:
1056.25 + -65x + x2 = -49.6 + 1056.25

Combine like terms: -49.6 + 1056.25 = 1006.65
1056.25 + -65x + x2 = 1006.65

Factor a perfect square on the left side:
(x + -32.5)(x + -32.5) = 1006.65

Calculate the square root of the right side: 31.727748108

Break this problem into two subproblems by setting 
(x + -32.5) equal to 31.727748108 and -31.727748108.

Subproblem 1
x + -32.5 = 31.727748108

Simplifying
x + -32.5 = 31.727748108

Reorder the terms:
-32.5 + x = 31.727748108

Solving
-32.5 + x = 31.727748108

Solving for variable 'x'.

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

Add '32.5' to each side of the equation.
-32.5 + 32.5 + x = 31.727748108 + 32.5

Combine like terms: -32.5 + 32.5 = 0.0
0.0 + x = 31.727748108 + 32.5
x = 31.727748108 + 32.5

Combine like terms: 31.727748108 + 32.5 = 64.227748108
x = 64.227748108

Simplifying
x = 64.227748108

Subproblem 2
x + -32.5 = -31.727748108

Simplifying
x + -32.5 = -31.727748108

Reorder the terms:
-32.5 + x = -31.727748108

Solving
-32.5 + x = -31.727748108

Solving for variable 'x'.

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

Add '32.5' to each side of the equation.
-32.5 + 32.5 + x = -31.727748108 + 32.5

Combine like terms: -32.5 + 32.5 = 0.0
0.0 + x = -31.727748108 + 32.5
x = -31.727748108 + 32.5

Combine like terms: -31.727748108 + 32.5 = 0.772251892
x = 0.772251892

Simplifying
x = 0.772251892

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {64.227748108, 0.772251892}
Solution
x = {64.227748108, 0.772251892}