5000=X(20X+100)

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Solution for 5000=X(20X+100) equation: 


Simplifying
5000 = X(20X + 100)

Reorder the terms:
5000 = X(100 + 20X)
5000 = (100 * X + 20X * X)
5000 = (100X + 20X2)

Solving
5000 = 100X + 20X2

Solving for variable 'X'.

Reorder the terms:
5000 + -100X + -20X2 = 100X + -100X + 20X2 + -20X2

Combine like terms: 100X + -100X = 0
5000 + -100X + -20X2 = 0 + 20X2 + -20X2
5000 + -100X + -20X2 = 20X2 + -20X2

Combine like terms: 20X2 + -20X2 = 0
5000 + -100X + -20X2 = 0

Factor out the Greatest Common Factor (GCF), '20'.
20(250 + -5X + -1X2) = 0

Ignore the factor 20.

Subproblem 1
Set the factor '(250 + -5X + -1X2)' equal to zero and attempt to solve:

Simplifying
250 + -5X + -1X2 = 0

Solving
250 + -5X + -1X2 = 0

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

Divide each side by '-1'.
-250 + 5X + X2 = 0

Move the constant term to the right:

Add '250' to each side of the equation.
-250 + 5X + 250 + X2 = 0 + 250

Reorder the terms:
-250 + 250 + 5X + X2 = 0 + 250

Combine like terms: -250 + 250 = 0
0 + 5X + X2 = 0 + 250
5X + X2 = 0 + 250

Combine like terms: 0 + 250 = 250
5X + X2 = 250

The X term is 5X.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5X + 6.25 + X2 = 250 + 6.25

Reorder the terms:
6.25 + 5X + X2 = 250 + 6.25

Combine like terms: 250 + 6.25 = 256.25
6.25 + 5X + X2 = 256.25

Factor a perfect square on the left side:
(X + 2.5)(X + 2.5) = 256.25

Calculate the square root of the right side: 16.007810594

Break this problem into two subproblems by setting 
(X + 2.5) equal to 16.007810594 and -16.007810594.


Subproblem 1
X + 2.5 = 16.007810594

Simplifying
X + 2.5 = 16.007810594

Reorder the terms:
2.5 + X = 16.007810594

Solving
2.5 + X = 16.007810594

Solving for variable 'X'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + X = 16.007810594 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + X = 16.007810594 + -2.5
X = 16.007810594 + -2.5

Combine like terms: 16.007810594 + -2.5 = 13.507810594
X = 13.507810594

Simplifying
X = 13.507810594


Subproblem 2
X + 2.5 = -16.007810594

Simplifying
X + 2.5 = -16.007810594

Reorder the terms:
2.5 + X = -16.007810594

Solving
2.5 + X = -16.007810594

Solving for variable 'X'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + X = -16.007810594 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + X = -16.007810594 + -2.5
X = -16.007810594 + -2.5

Combine like terms: -16.007810594 + -2.5 = -18.507810594
X = -18.507810594

Simplifying
X = -18.507810594


Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {13.507810594, -18.507810594}
Solution
X = {13.507810594, -18.507810594}

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