x^2+0.00018x-0.00015894=0

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Solution for x^2+0.00018x-0.00015894=0 equation: 


Simplifying
x2 + 0.00018x + -0.00015894 = 0

Reorder the terms:
-0.00015894 + 0.00018x + x2 = 0

Solving
-0.00015894 + 0.00018x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '0.00015894' to each side of the equation.
-0.00015894 + 0.00018x + 0.00015894 + x2 = 0 + 0.00015894

Reorder the terms:
-0.00015894 + 0.00015894 + 0.00018x + x2 = 0 + 0.00015894

Combine like terms: -0.00015894 + 0.00015894 = 0.00000000
0.00000000 + 0.00018x + x2 = 0 + 0.00015894
0.00018x + x2 = 0 + 0.00015894

Combine like terms: 0 + 0.00015894 = 0.00015894
0.00018x + x2 = 0.00015894

The x term is 0.00018x.  Take half its coefficient (0.00009).
Square it (0.0000000081) and add it to both sides.

Add '0.0000000081' to each side of the equation.
0.00018x + 0.0000000081 + x2 = 0.00015894 + 0.0000000081

Reorder the terms:
0.0000000081 + 0.00018x + x2 = 0.00015894 + 0.0000000081

Combine like terms: 0.00015894 + 0.0000000081 = 0.0001589481
0.0000000081 + 0.00018x + x2 = 0.0001589481

Factor a perfect square on the left side:
(x + 0.00009)(x + 0.00009) = 0.0001589481

Calculate the square root of the right side: 0.012607462

Break this problem into two subproblems by setting 
(x + 0.00009) equal to 0.012607462 and -0.012607462.


Subproblem 1
x + 0.00009 = 0.012607462

Simplifying
x + 0.00009 = 0.012607462

Reorder the terms:
0.00009 + x = 0.012607462

Solving
0.00009 + x = 0.012607462

Solving for variable 'x'.

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

Add '-0.00009' to each side of the equation.
0.00009 + -0.00009 + x = 0.012607462 + -0.00009

Combine like terms: 0.00009 + -0.00009 = 0.00000
0.00000 + x = 0.012607462 + -0.00009
x = 0.012607462 + -0.00009

Combine like terms: 0.012607462 + -0.00009 = 0.012517462
x = 0.012517462

Simplifying
x = 0.012517462


Subproblem 2
x + 0.00009 = -0.012607462

Simplifying
x + 0.00009 = -0.012607462

Reorder the terms:
0.00009 + x = -0.012607462

Solving
0.00009 + x = -0.012607462

Solving for variable 'x'.

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

Add '-0.00009' to each side of the equation.
0.00009 + -0.00009 + x = -0.012607462 + -0.00009

Combine like terms: 0.00009 + -0.00009 = 0.00000
0.00000 + x = -0.012607462 + -0.00009
x = -0.012607462 + -0.00009

Combine like terms: -0.012607462 + -0.00009 = -0.012697462
x = -0.012697462

Simplifying
x = -0.012697462


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.012517462, -0.012697462}

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