(x^2+1000x)=0.16

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Solution for (x^2+1000x)=0.16 equation: 


Simplifying
(x2 + 1000x) = 0.16

Reorder the terms:
(1000x + x2) = 0.16

Remove parenthesis around (1000x + x2)
1000x + x2 = 0.16

Solving
1000x + x2 = 0.16

Solving for variable 'x'.

Reorder the terms:
-0.16 + 1000x + x2 = 0.16 + -0.16

Combine like terms: 0.16 + -0.16 = 0.00
-0.16 + 1000x + x2 = 0.00

Begin completing the square.

Move the constant term to the right:

Add '0.16' to each side of the equation.
-0.16 + 1000x + 0.16 + x2 = 0.00 + 0.16

Reorder the terms:
-0.16 + 0.16 + 1000x + x2 = 0.00 + 0.16

Combine like terms: -0.16 + 0.16 = 0.00
0.00 + 1000x + x2 = 0.00 + 0.16
1000x + x2 = 0.00 + 0.16

Combine like terms: 0.00 + 0.16 = 0.16
1000x + x2 = 0.16

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 = 0.16 + 250000

Reorder the terms:
250000 + 1000x + x2 = 0.16 + 250000

Combine like terms: 0.16 + 250000 = 250000.16
250000 + 1000x + x2 = 250000.16

Factor a perfect square on the left side:
(x + 500)(x + 500) = 250000.16

Calculate the square root of the right side: 500.00016

Break this problem into two subproblems by setting 
(x + 500) equal to 500.00016 and -500.00016.


Subproblem 1
x + 500 = 500.00016

Simplifying
x + 500 = 500.00016

Reorder the terms:
500 + x = 500.00016

Solving
500 + x = 500.00016

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 = 500.00016 + -500

Combine like terms: 500 + -500 = 0
0 + x = 500.00016 + -500
x = 500.00016 + -500

Combine like terms: 500.00016 + -500 = 0.00016
x = 0.00016

Simplifying
x = 0.00016


Subproblem 2
x + 500 = -500.00016

Simplifying
x + 500 = -500.00016

Reorder the terms:
500 + x = -500.00016

Solving
500 + x = -500.00016

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 = -500.00016 + -500

Combine like terms: 500 + -500 = 0
0 + x = -500.00016 + -500
x = -500.00016 + -500

Combine like terms: -500.00016 + -500 = -1000.00016
x = -1000.00016

Simplifying
x = -1000.00016


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.00016, -1000.00016}

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