x^2+0.000018x-0.0000018=0

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Solution for x^2+0.000018x-0.0000018=0 equation: 


Simplifying
x2 + 0.000018x + -0.0000018 = 0

Reorder the terms:
-0.0000018 + 0.000018x + x2 = 0

Solving
-0.0000018 + 0.000018x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '0.0000018' to each side of the equation.
-0.0000018 + 0.000018x + 0.0000018 + x2 = 0 + 0.0000018

Reorder the terms:
-0.0000018 + 0.0000018 + 0.000018x + x2 = 0 + 0.0000018

Combine like terms: -0.0000018 + 0.0000018 = 0.0000000
0.0000000 + 0.000018x + x2 = 0 + 0.0000018
0.000018x + x2 = 0 + 0.0000018

Combine like terms: 0 + 0.0000018 = 0.0000018
0.000018x + x2 = 0.0000018

The x term is 0.000018x.  Take half its coefficient (0.000009).
Square it (0.000000000081) and add it to both sides.

Add '0.000000000081' to each side of the equation.
0.000018x + 0.000000000081 + x2 = 0.0000018 + 0.000000000081

Reorder the terms:
0.000000000081 + 0.000018x + x2 = 0.0000018 + 0.000000000081

Combine like terms: 0.0000018 + 0.000000000081 = 0.000001800081
0.000000000081 + 0.000018x + x2 = 0.000001800081

Factor a perfect square on the left side:
(x + 0.000009)(x + 0.000009) = 0.000001800081

Calculate the square root of the right side: 0.001341671

Break this problem into two subproblems by setting 
(x + 0.000009) equal to 0.001341671 and -0.001341671.


Subproblem 1
x + 0.000009 = 0.001341671

Simplifying
x + 0.000009 = 0.001341671

Reorder the terms:
0.000009 + x = 0.001341671

Solving
0.000009 + x = 0.001341671

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-0.000009' to each side of the equation.
0.000009 + -0.000009 + x = 0.001341671 + -0.000009

Combine like terms: 0.000009 + -0.000009 = 0.000000
0.000000 + x = 0.001341671 + -0.000009
x = 0.001341671 + -0.000009

Combine like terms: 0.001341671 + -0.000009 = 0.001332671
x = 0.001332671

Simplifying
x = 0.001332671


Subproblem 2
x + 0.000009 = -0.001341671

Simplifying
x + 0.000009 = -0.001341671

Reorder the terms:
0.000009 + x = -0.001341671

Solving
0.000009 + x = -0.001341671

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-0.000009' to each side of the equation.
0.000009 + -0.000009 + x = -0.001341671 + -0.000009

Combine like terms: 0.000009 + -0.000009 = 0.000000
0.000000 + x = -0.001341671 + -0.000009
x = -0.001341671 + -0.000009

Combine like terms: -0.001341671 + -0.000009 = -0.001350671
x = -0.001350671

Simplifying
x = -0.001350671


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.001332671, -0.001350671}

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