0=35x(1-0.001x)+1500

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Solution for 0=35x(1-0.001x)+1500 equation:


Simplifying
0 = 35x(1 + -0.001x) + 1500
0 = (1 * 35x + -0.001x * 35x) + 1500
0 = (35x + -0.035x2) + 1500

Reorder the terms:
0 = 1500 + 35x + -0.035x2

Solving
0 = 1500 + 35x + -0.035x2

Solving for variable 'x'.

Combine like terms: 0 + -1500 = -1500
-1500 + -35x + 0.035x2 = 1500 + 35x + -0.035x2 + -1500 + -35x + 0.035x2

Reorder the terms:
-1500 + -35x + 0.035x2 = 1500 + -1500 + 35x + -35x + -0.035x2 + 0.035x2

Combine like terms: 1500 + -1500 = 0
-1500 + -35x + 0.035x2 = 0 + 35x + -35x + -0.035x2 + 0.035x2
-1500 + -35x + 0.035x2 = 35x + -35x + -0.035x2 + 0.035x2

Combine like terms: 35x + -35x = 0
-1500 + -35x + 0.035x2 = 0 + -0.035x2 + 0.035x2
-1500 + -35x + 0.035x2 = -0.035x2 + 0.035x2

Combine like terms: -0.035x2 + 0.035x2 = 0.000
-1500 + -35x + 0.035x2 = 0.000

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

Divide each side by '0.035'.
-42857.14286 + -1000x + x2 = 0

Move the constant term to the right:

Add '42857.14286' to each side of the equation.
-42857.14286 + -1000x + 42857.14286 + x2 = 0 + 42857.14286

Reorder the terms:
-42857.14286 + 42857.14286 + -1000x + x2 = 0 + 42857.14286

Combine like terms: -42857.14286 + 42857.14286 = 0.00000
0.00000 + -1000x + x2 = 0 + 42857.14286
-1000x + x2 = 0 + 42857.14286

Combine like terms: 0 + 42857.14286 = 42857.14286
-1000x + x2 = 42857.14286

The x term is -1000x.  Take half its coefficient (-500).
Square it (250000) and add it to both sides.

Add '250000' to each side of the equation.
-1000x + 250000 + x2 = 42857.14286 + 250000

Reorder the terms:
250000 + -1000x + x2 = 42857.14286 + 250000

Combine like terms: 42857.14286 + 250000 = 292857.14286
250000 + -1000x + x2 = 292857.14286

Factor a perfect square on the left side:
(x + -500)(x + -500) = 292857.14286

Calculate the square root of the right side: 541.162769285

Break this problem into two subproblems by setting 
(x + -500) equal to 541.162769285 and -541.162769285.

Subproblem 1

x + -500 = 541.162769285 Simplifying x + -500 = 541.162769285 Reorder the terms: -500 + x = 541.162769285 Solving -500 + x = 541.162769285 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '500' to each side of the equation. -500 + 500 + x = 541.162769285 + 500 Combine like terms: -500 + 500 = 0 0 + x = 541.162769285 + 500 x = 541.162769285 + 500 Combine like terms: 541.162769285 + 500 = 1041.162769285 x = 1041.162769285 Simplifying x = 1041.162769285

Subproblem 2

x + -500 = -541.162769285 Simplifying x + -500 = -541.162769285 Reorder the terms: -500 + x = -541.162769285 Solving -500 + x = -541.162769285 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '500' to each side of the equation. -500 + 500 + x = -541.162769285 + 500 Combine like terms: -500 + 500 = 0 0 + x = -541.162769285 + 500 x = -541.162769285 + 500 Combine like terms: -541.162769285 + 500 = -41.162769285 x = -41.162769285 Simplifying x = -41.162769285

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1041.162769285, -41.162769285}

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