(-x^2)+(.000004)-(.00002x)=0

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Solution for (-x^2)+(.000004)-(.00002x)=0 equation:


Simplifying
(-1x2) + (0.000004) + -1(0.00002x) = 0
(-1x2) + 0.000004 + -1(0.00002x) = 0

Remove parenthesis around (0.00002x)
(-1x2) + 0.000004 + -1 * 0.00002x = 0

Multiply -1 * 0.00002
(-1x2) + 0.000004 + -0.00002x = 0

Reorder the terms:
0.000004 + -0.00002x + (-1x2) = 0

Solving
0.000004 + -0.00002x + (-1x2) = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-0.000004 + 0.00002x + x2 = 0

Move the constant term to the right:

Add '0.000004' to each side of the equation.
-0.000004 + 0.00002x + 0.000004 + x2 = 0 + 0.000004

Reorder the terms:
-0.000004 + 0.000004 + 0.00002x + x2 = 0 + 0.000004

Combine like terms: -0.000004 + 0.000004 = 0.000000
0.000000 + 0.00002x + x2 = 0 + 0.000004
0.00002x + x2 = 0 + 0.000004

Combine like terms: 0 + 0.000004 = 0.000004
0.00002x + x2 = 0.000004

The x term is 0.00002x.  Take half its coefficient (0.00001).
Square it (0.0000000001) and add it to both sides.

Add '0.0000000001' to each side of the equation.
0.00002x + 0.0000000001 + x2 = 0.000004 + 0.0000000001

Reorder the terms:
0.0000000001 + 0.00002x + x2 = 0.000004 + 0.0000000001

Combine like terms: 0.000004 + 0.0000000001 = 0.0000040001
0.0000000001 + 0.00002x + x2 = 0.0000040001

Factor a perfect square on the left side:
((x) + 0.00001)((x) + 0.00001) = 0.0000040001

Calculate the square root of the right side: 0.002000025

Break this problem into two subproblems by setting 
((x) + 0.00001) equal to 0.002000025 and -0.002000025.

Subproblem 1

(x) + 0.00001 = 0.002000025 Simplifying (x) + 0.00001 = 0.002000025 x + 0.00001 = 0.002000025 Reorder the terms: 0.00001 + x = 0.002000025 Solving 0.00001 + x = 0.002000025 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.00001' to each side of the equation. 0.00001 + -0.00001 + x = 0.002000025 + -0.00001 Combine like terms: 0.00001 + -0.00001 = 0.00000 0.00000 + x = 0.002000025 + -0.00001 x = 0.002000025 + -0.00001 Combine like terms: 0.002000025 + -0.00001 = 0.001990025 x = 0.001990025 Simplifying x = 0.001990025

Subproblem 2

(x) + 0.00001 = -0.002000025 Simplifying (x) + 0.00001 = -0.002000025 x + 0.00001 = -0.002000025 Reorder the terms: 0.00001 + x = -0.002000025 Solving 0.00001 + x = -0.002000025 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.00001' to each side of the equation. 0.00001 + -0.00001 + x = -0.002000025 + -0.00001 Combine like terms: 0.00001 + -0.00001 = 0.00000 0.00000 + x = -0.002000025 + -0.00001 x = -0.002000025 + -0.00001 Combine like terms: -0.002000025 + -0.00001 = -0.002010025 x = -0.002010025 Simplifying x = -0.002010025

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.001990025, -0.002010025}

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