(-x^2)+(.00000000018)-(.00000003x)=0

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Solution for (-x^2)+(.00000000018)-(.00000003x)=0 equation:


Simplifying
(-1x2) + (0.00000000018) + -1(0.00000003x) = 0
(-1x2) + 0.00000000018 + -1(0.00000003x) = 0

Remove parenthesis around (0.00000003x)
(-1x2) + 0.00000000018 + -1 * 0.00000003x = 0

Multiply -1 * 0.00000003
(-1x2) + 0.00000000018 + -0.00000003x = 0

Reorder the terms:
0.00000000018 + -0.00000003x + (-1x2) = 0

Solving
0.00000000018 + -0.00000003x + (-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'.
-0.00000000018 + 0.00000003x + x2 = 0

Move the constant term to the right:

Add '0.00000000018' to each side of the equation.
-0.00000000018 + 0.00000003x + 0.00000000018 + x2 = 0 + 0.00000000018

Reorder the terms:
-0.00000000018 + 0.00000000018 + 0.00000003x + x2 = 0 + 0.00000000018

Combine like terms: -0.00000000018 + 0.00000000018 = 0.00000000000
0.00000000000 + 0.00000003x + x2 = 0 + 0.00000000018
0.00000003x + x2 = 0 + 0.00000000018

Combine like terms: 0 + 0.00000000018 = 0.00000000018
0.00000003x + x2 = 0.00000000018

The x term is 0.00000003x.  Take half its coefficient (0.000000015).
Square it (0.000000000000000225) and add it to both sides.

Add '0.000000000000000225' to each side of the equation.
0.00000003x + 0.000000000000000225 + x2 = 0.00000000018 + 0.000000000000000225

Reorder the terms:
0.000000000000000225 + 0.00000003x + x2 = 0.00000000018 + 0.000000000000000225

Combine like terms: 0.00000000018 + 0.000000000000000225 = 0.000000000180000225
0.000000000000000225 + 0.00000003x + x2 = 0.000000000180000225

Factor a perfect square on the left side:
((x) + 0.000000015)((x) + 0.000000015) = 0.000000000180000225

Calculate the square root of the right side: 0.000013416

Break this problem into two subproblems by setting 
((x) + 0.000000015) equal to 0.000013416 and -0.000013416.

Subproblem 1

(x) + 0.000000015 = 0.000013416 Simplifying (x) + 0.000000015 = 0.000013416 x + 0.000000015 = 0.000013416 Reorder the terms: 0.000000015 + x = 0.000013416 Solving 0.000000015 + x = 0.000013416 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.000000015' to each side of the equation. 0.000000015 + -0.000000015 + x = 0.000013416 + -0.000000015 Combine like terms: 0.000000015 + -0.000000015 = 0.000000000 0.000000000 + x = 0.000013416 + -0.000000015 x = 0.000013416 + -0.000000015 Combine like terms: 0.000013416 + -0.000000015 = 0.000013401 x = 0.000013401 Simplifying x = 0.000013401

Subproblem 2

(x) + 0.000000015 = -0.000013416 Simplifying (x) + 0.000000015 = -0.000013416 x + 0.000000015 = -0.000013416 Reorder the terms: 0.000000015 + x = -0.000013416 Solving 0.000000015 + x = -0.000013416 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.000000015' to each side of the equation. 0.000000015 + -0.000000015 + x = -0.000013416 + -0.000000015 Combine like terms: 0.000000015 + -0.000000015 = 0.000000000 0.000000000 + x = -0.000013416 + -0.000000015 x = -0.000013416 + -0.000000015 Combine like terms: -0.000013416 + -0.000000015 = -0.000013431 x = -0.000013431 Simplifying x = -0.000013431

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.000013401, -0.000013431}

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