13000=0.02x(1650-x)

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Solution for 13000=0.02x(1650-x) equation:


Simplifying
13000 = 0.02x(1650 + -1x)
13000 = (1650 * 0.02x + -1x * 0.02x)
13000 = (33x + -0.02x2)

Solving
13000 = 33x + -0.02x2

Solving for variable 'x'.

Reorder the terms:
13000 + -33x + 0.02x2 = 33x + -33x + -0.02x2 + 0.02x2

Combine like terms: 33x + -33x = 0
13000 + -33x + 0.02x2 = 0 + -0.02x2 + 0.02x2
13000 + -33x + 0.02x2 = -0.02x2 + 0.02x2

Combine like terms: -0.02x2 + 0.02x2 = 0.00
13000 + -33x + 0.02x2 = 0.00

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

Divide each side by '0.02'.
650000 + -1650x + x2 = 0

Move the constant term to the right:

Add '-650000' to each side of the equation.
650000 + -1650x + -650000 + x2 = 0 + -650000

Reorder the terms:
650000 + -650000 + -1650x + x2 = 0 + -650000

Combine like terms: 650000 + -650000 = 0
0 + -1650x + x2 = 0 + -650000
-1650x + x2 = 0 + -650000

Combine like terms: 0 + -650000 = -650000
-1650x + x2 = -650000

The x term is -1650x.  Take half its coefficient (-825).
Square it (680625) and add it to both sides.

Add '680625' to each side of the equation.
-1650x + 680625 + x2 = -650000 + 680625

Reorder the terms:
680625 + -1650x + x2 = -650000 + 680625

Combine like terms: -650000 + 680625 = 30625
680625 + -1650x + x2 = 30625

Factor a perfect square on the left side:
(x + -825)(x + -825) = 30625

Calculate the square root of the right side: 175

Break this problem into two subproblems by setting 
(x + -825) equal to 175 and -175.

Subproblem 1

x + -825 = 175 Simplifying x + -825 = 175 Reorder the terms: -825 + x = 175 Solving -825 + x = 175 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '825' to each side of the equation. -825 + 825 + x = 175 + 825 Combine like terms: -825 + 825 = 0 0 + x = 175 + 825 x = 175 + 825 Combine like terms: 175 + 825 = 1000 x = 1000 Simplifying x = 1000

Subproblem 2

x + -825 = -175 Simplifying x + -825 = -175 Reorder the terms: -825 + x = -175 Solving -825 + x = -175 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '825' to each side of the equation. -825 + 825 + x = -175 + 825 Combine like terms: -825 + 825 = 0 0 + x = -175 + 825 x = -175 + 825 Combine like terms: -175 + 825 = 650 x = 650 Simplifying x = 650

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1000, 650}

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