0.001x(x-5)=100

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Solution for 0.001x(x-5)=100 equation:


Simplifying
0.001x(x + -5) = 100

Reorder the terms:
0.001x(-5 + x) = 100
(-5 * 0.001x + x * 0.001x) = 100
(-0.005x + 0.001x2) = 100

Solving
-0.005x + 0.001x2 = 100

Solving for variable 'x'.

Reorder the terms:
-100 + -0.005x + 0.001x2 = 100 + -100

Combine like terms: 100 + -100 = 0
-100 + -0.005x + 0.001x2 = 0

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

Divide each side by '0.001'.
-100000 + -5x + x2 = 0

Move the constant term to the right:

Add '100000' to each side of the equation.
-100000 + -5x + 100000 + x2 = 0 + 100000

Reorder the terms:
-100000 + 100000 + -5x + x2 = 0 + 100000

Combine like terms: -100000 + 100000 = 0
0 + -5x + x2 = 0 + 100000
-5x + x2 = 0 + 100000

Combine like terms: 0 + 100000 = 100000
-5x + x2 = 100000

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 = 100000 + 6.25

Reorder the terms:
6.25 + -5x + x2 = 100000 + 6.25

Combine like terms: 100000 + 6.25 = 100006.25
6.25 + -5x + x2 = 100006.25

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 100006.25

Calculate the square root of the right side: 316.23764798

Break this problem into two subproblems by setting 
(x + -2.5) equal to 316.23764798 and -316.23764798.

Subproblem 1

x + -2.5 = 316.23764798 Simplifying x + -2.5 = 316.23764798 Reorder the terms: -2.5 + x = 316.23764798 Solving -2.5 + x = 316.23764798 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 = 316.23764798 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 316.23764798 + 2.5 x = 316.23764798 + 2.5 Combine like terms: 316.23764798 + 2.5 = 318.73764798 x = 318.73764798 Simplifying x = 318.73764798

Subproblem 2

x + -2.5 = -316.23764798 Simplifying x + -2.5 = -316.23764798 Reorder the terms: -2.5 + x = -316.23764798 Solving -2.5 + x = -316.23764798 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 = -316.23764798 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -316.23764798 + 2.5 x = -316.23764798 + 2.5 Combine like terms: -316.23764798 + 2.5 = -313.73764798 x = -313.73764798 Simplifying x = -313.73764798

Solution

The solution to the problem is based on the solutions from the subproblems. x = {318.73764798, -313.73764798}

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