x^2+0.000018x-0.0000036=0

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Solution for x^2+0.000018x-0.0000036=0 equation:


Simplifying
x2 + 0.000018x + -0.0000036 = 0

Reorder the terms:
-0.0000036 + 0.000018x + x2 = 0

Solving
-0.0000036 + 0.000018x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '0.0000036' to each side of the equation.
-0.0000036 + 0.000018x + 0.0000036 + x2 = 0 + 0.0000036

Reorder the terms:
-0.0000036 + 0.0000036 + 0.000018x + x2 = 0 + 0.0000036

Combine like terms: -0.0000036 + 0.0000036 = 0.0000000
0.0000000 + 0.000018x + x2 = 0 + 0.0000036
0.000018x + x2 = 0 + 0.0000036

Combine like terms: 0 + 0.0000036 = 0.0000036
0.000018x + x2 = 0.0000036

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 = 0.0000036 + 0.000000000081

Reorder the terms:
0.000000000081 + 0.000018x + x2 = 0.0000036 + 0.000000000081

Combine like terms: 0.0000036 + 0.000000000081 = 0.000003600081
0.000000000081 + 0.000018x + x2 = 0.000003600081

Factor a perfect square on the left side:
(x + 0.000009)(x + 0.000009) = 0.000003600081

Calculate the square root of the right side: 0.001897388

Break this problem into two subproblems by setting 
(x + 0.000009) equal to 0.001897388 and -0.001897388.

Subproblem 1

x + 0.000009 = 0.001897388 Simplifying x + 0.000009 = 0.001897388 Reorder the terms: 0.000009 + x = 0.001897388 Solving 0.000009 + x = 0.001897388 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 = 0.001897388 + -0.000009 Combine like terms: 0.000009 + -0.000009 = 0.000000 0.000000 + x = 0.001897388 + -0.000009 x = 0.001897388 + -0.000009 Combine like terms: 0.001897388 + -0.000009 = 0.001888388 x = 0.001888388 Simplifying x = 0.001888388

Subproblem 2

x + 0.000009 = -0.001897388 Simplifying x + 0.000009 = -0.001897388 Reorder the terms: 0.000009 + x = -0.001897388 Solving 0.000009 + x = -0.001897388 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 = -0.001897388 + -0.000009 Combine like terms: 0.000009 + -0.000009 = 0.000000 0.000000 + x = -0.001897388 + -0.000009 x = -0.001897388 + -0.000009 Combine like terms: -0.001897388 + -0.000009 = -0.001906388 x = -0.001906388 Simplifying x = -0.001906388

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.001888388, -0.001906388}

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