-0.0006(x)(x-200)=5

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Solution for -0.0006(x)(x-200)=5 equation:


Simplifying
-0.0006(x)(x + -200) = 5

Reorder the terms:
-0.0006x(-200 + x) = 5
(-200 * -0.0006x + x * -0.0006x) = 5
(0.12x + -0.0006x2) = 5

Solving
0.12x + -0.0006x2 = 5

Solving for variable 'x'.

Reorder the terms:
-5 + 0.12x + -0.0006x2 = 5 + -5

Combine like terms: 5 + -5 = 0
-5 + 0.12x + -0.0006x2 = 0

Begin completing the square.  Divide all terms by
-0.0006 the coefficient of the squared term: 

Divide each side by '-0.0006'.
8333.333333 + -200x + x2 = 0

Move the constant term to the right:

Add '-8333.333333' to each side of the equation.
8333.333333 + -200x + -8333.333333 + x2 = 0 + -8333.333333

Reorder the terms:
8333.333333 + -8333.333333 + -200x + x2 = 0 + -8333.333333

Combine like terms: 8333.333333 + -8333.333333 = 0.000000
0.000000 + -200x + x2 = 0 + -8333.333333
-200x + x2 = 0 + -8333.333333

Combine like terms: 0 + -8333.333333 = -8333.333333
-200x + x2 = -8333.333333

The x term is -200x.  Take half its coefficient (-100).
Square it (10000) and add it to both sides.

Add '10000' to each side of the equation.
-200x + 10000 + x2 = -8333.333333 + 10000

Reorder the terms:
10000 + -200x + x2 = -8333.333333 + 10000

Combine like terms: -8333.333333 + 10000 = 1666.666667
10000 + -200x + x2 = 1666.666667

Factor a perfect square on the left side:
(x + -100)(x + -100) = 1666.666667

Calculate the square root of the right side: 40.82482905

Break this problem into two subproblems by setting 
(x + -100) equal to 40.82482905 and -40.82482905.

Subproblem 1

x + -100 = 40.82482905 Simplifying x + -100 = 40.82482905 Reorder the terms: -100 + x = 40.82482905 Solving -100 + x = 40.82482905 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '100' to each side of the equation. -100 + 100 + x = 40.82482905 + 100 Combine like terms: -100 + 100 = 0 0 + x = 40.82482905 + 100 x = 40.82482905 + 100 Combine like terms: 40.82482905 + 100 = 140.82482905 x = 140.82482905 Simplifying x = 140.82482905

Subproblem 2

x + -100 = -40.82482905 Simplifying x + -100 = -40.82482905 Reorder the terms: -100 + x = -40.82482905 Solving -100 + x = -40.82482905 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '100' to each side of the equation. -100 + 100 + x = -40.82482905 + 100 Combine like terms: -100 + 100 = 0 0 + x = -40.82482905 + 100 x = -40.82482905 + 100 Combine like terms: -40.82482905 + 100 = 59.17517095 x = 59.17517095 Simplifying x = 59.17517095

Solution

The solution to the problem is based on the solutions from the subproblems. x = {140.82482905, 59.17517095}

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