15x+10000=-2x^2+600x

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Solution for 15x+10000=-2x^2+600x equation:


Simplifying
15x + 10000 = -2x2 + 600x

Reorder the terms:
10000 + 15x = -2x2 + 600x

Reorder the terms:
10000 + 15x = 600x + -2x2

Solving
10000 + 15x = 600x + -2x2

Solving for variable 'x'.

Combine like terms: 15x + -600x = -585x
10000 + -585x + 2x2 = 600x + -2x2 + -600x + 2x2

Reorder the terms:
10000 + -585x + 2x2 = 600x + -600x + -2x2 + 2x2

Combine like terms: 600x + -600x = 0
10000 + -585x + 2x2 = 0 + -2x2 + 2x2
10000 + -585x + 2x2 = -2x2 + 2x2

Combine like terms: -2x2 + 2x2 = 0
10000 + -585x + 2x2 = 0

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

Divide each side by '2'.
5000 + -292.5x + x2 = 0

Move the constant term to the right:

Add '-5000' to each side of the equation.
5000 + -292.5x + -5000 + x2 = 0 + -5000

Reorder the terms:
5000 + -5000 + -292.5x + x2 = 0 + -5000

Combine like terms: 5000 + -5000 = 0
0 + -292.5x + x2 = 0 + -5000
-292.5x + x2 = 0 + -5000

Combine like terms: 0 + -5000 = -5000
-292.5x + x2 = -5000

The x term is -292.5x.  Take half its coefficient (-146.25).
Square it (21389.0625) and add it to both sides.

Add '21389.0625' to each side of the equation.
-292.5x + 21389.0625 + x2 = -5000 + 21389.0625

Reorder the terms:
21389.0625 + -292.5x + x2 = -5000 + 21389.0625

Combine like terms: -5000 + 21389.0625 = 16389.0625
21389.0625 + -292.5x + x2 = 16389.0625

Factor a perfect square on the left side:
(x + -146.25)(x + -146.25) = 16389.0625

Calculate the square root of the right side: 128.019773863

Break this problem into two subproblems by setting 
(x + -146.25) equal to 128.019773863 and -128.019773863.

Subproblem 1

x + -146.25 = 128.019773863 Simplifying x + -146.25 = 128.019773863 Reorder the terms: -146.25 + x = 128.019773863 Solving -146.25 + x = 128.019773863 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '146.25' to each side of the equation. -146.25 + 146.25 + x = 128.019773863 + 146.25 Combine like terms: -146.25 + 146.25 = 0.00 0.00 + x = 128.019773863 + 146.25 x = 128.019773863 + 146.25 Combine like terms: 128.019773863 + 146.25 = 274.269773863 x = 274.269773863 Simplifying x = 274.269773863

Subproblem 2

x + -146.25 = -128.019773863 Simplifying x + -146.25 = -128.019773863 Reorder the terms: -146.25 + x = -128.019773863 Solving -146.25 + x = -128.019773863 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '146.25' to each side of the equation. -146.25 + 146.25 + x = -128.019773863 + 146.25 Combine like terms: -146.25 + 146.25 = 0.00 0.00 + x = -128.019773863 + 146.25 x = -128.019773863 + 146.25 Combine like terms: -128.019773863 + 146.25 = 18.230226137 x = 18.230226137 Simplifying x = 18.230226137

Solution

The solution to the problem is based on the solutions from the subproblems. x = {274.269773863, 18.230226137}

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