2000+46x=2x^2

Solution for 2000+46x=2x^2 equation:

Simplifying
2000 + 46x = 2x2

Solving
2000 + 46x = 2x2

Solving for variable 'x'.

Combine like terms: 2x2 + -2x2 = 0
2000 + 46x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(1000 + 23x + -1x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(1000 + 23x + -1x2)' equal to zero and attempt to solve:

Simplifying
1000 + 23x + -1x2 = 0

Solving
1000 + 23x + -1x2 = 0

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

Divide each side by '-1'.
-1000 + -23x + x2 = 0

Move the constant term to the right:

Add '1000' to each side of the equation.
-1000 + -23x + 1000 + x2 = 0 + 1000

Reorder the terms:
-1000 + 1000 + -23x + x2 = 0 + 1000

Combine like terms: -1000 + 1000 = 0
0 + -23x + x2 = 0 + 1000
-23x + x2 = 0 + 1000

Combine like terms: 0 + 1000 = 1000
-23x + x2 = 1000

The x term is -23x.  Take half its coefficient (-11.5).
Square it (132.25) and add it to both sides.

Add '132.25' to each side of the equation.
-23x + 132.25 + x2 = 1000 + 132.25

Reorder the terms:
132.25 + -23x + x2 = 1000 + 132.25

Combine like terms: 1000 + 132.25 = 1132.25
132.25 + -23x + x2 = 1132.25

Factor a perfect square on the left side:
(x + -11.5)(x + -11.5) = 1132.25

Calculate the square root of the right side: 33.648922717

Break this problem into two subproblems by setting 
(x + -11.5) equal to 33.648922717 and -33.648922717.

Subproblem 1
x + -11.5 = 33.648922717

Simplifying
x + -11.5 = 33.648922717

Reorder the terms:
-11.5 + x = 33.648922717

Solving
-11.5 + x = 33.648922717

Solving for variable 'x'.

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

Add '11.5' to each side of the equation.
-11.5 + 11.5 + x = 33.648922717 + 11.5

Combine like terms: -11.5 + 11.5 = 0.0
0.0 + x = 33.648922717 + 11.5
x = 33.648922717 + 11.5

Combine like terms: 33.648922717 + 11.5 = 45.148922717
x = 45.148922717

Simplifying
x = 45.148922717

Subproblem 2
x + -11.5 = -33.648922717

Simplifying
x + -11.5 = -33.648922717

Reorder the terms:
-11.5 + x = -33.648922717

Solving
-11.5 + x = -33.648922717

Solving for variable 'x'.

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

Add '11.5' to each side of the equation.
-11.5 + 11.5 + x = -33.648922717 + 11.5

Combine like terms: -11.5 + 11.5 = 0.0
0.0 + x = -33.648922717 + 11.5
x = -33.648922717 + 11.5

Combine like terms: -33.648922717 + 11.5 = -22.148922717
x = -22.148922717

Simplifying
x = -22.148922717

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {45.148922717, -22.148922717}
Solution
x = {45.148922717, -22.148922717}