200*x-200(x+5)=2*x(x+5)

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Solution for 200*x-200(x+5)=2*x(x+5) equation: 


Simplifying
200x + -200(x + 5) = 2x(x + 5)

Reorder the terms:
200x + -200(5 + x) = 2x(x + 5)
200x + (5 * -200 + x * -200) = 2x(x + 5)
200x + (-1000 + -200x) = 2x(x + 5)

Reorder the terms:
-1000 + 200x + -200x = 2x(x + 5)

Combine like terms: 200x + -200x = 0
-1000 + 0 = 2x(x + 5)
-1000 = 2x(x + 5)

Reorder the terms:
-1000 = 2x(5 + x)
-1000 = (5 * 2x + x * 2x)
-1000 = (10x + 2x2)

Solving
-1000 = 10x + 2x2

Solving for variable 'x'.

Reorder the terms:
-1000 + -10x + -2x2 = 10x + -10x + 2x2 + -2x2

Combine like terms: 10x + -10x = 0
-1000 + -10x + -2x2 = 0 + 2x2 + -2x2
-1000 + -10x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-1000 + -10x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '-2'.
-2(500 + 5x + x2) = 0

Ignore the factor -2.

Subproblem 1
Set the factor '(500 + 5x + x2)' equal to zero and attempt to solve:

Simplifying
500 + 5x + x2 = 0

Solving
500 + 5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-500' to each side of the equation.
500 + 5x + -500 + x2 = 0 + -500

Reorder the terms:
500 + -500 + 5x + x2 = 0 + -500

Combine like terms: 500 + -500 = 0
0 + 5x + x2 = 0 + -500
5x + x2 = 0 + -500

Combine like terms: 0 + -500 = -500
5x + x2 = -500

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 = -500 + 6.25

Reorder the terms:
6.25 + 5x + x2 = -500 + 6.25

Combine like terms: -500 + 6.25 = -493.75
6.25 + 5x + x2 = -493.75

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = -493.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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