x^2+0.00000003x-0.000000003=0

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Solution for x^2+0.00000003x-0.000000003=0 equation:


Simplifying
x2 + 0.00000003x + -0.000000003 = 0

Reorder the terms:
-0.000000003 + 0.00000003x + x2 = 0

Solving
-0.000000003 + 0.00000003x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '0.000000003' to each side of the equation.
-0.000000003 + 0.00000003x + 0.000000003 + x2 = 0 + 0.000000003

Reorder the terms:
-0.000000003 + 0.000000003 + 0.00000003x + x2 = 0 + 0.000000003

Combine like terms: -0.000000003 + 0.000000003 = 0.000000000
0.000000000 + 0.00000003x + x2 = 0 + 0.000000003
0.00000003x + x2 = 0 + 0.000000003

Combine like terms: 0 + 0.000000003 = 0.000000003
0.00000003x + x2 = 0.000000003

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 = 0.000000003 + 0.000000000000000225

Reorder the terms:
0.000000000000000225 + 0.00000003x + x2 = 0.000000003 + 0.000000000000000225

Combine like terms: 0.000000003 + 0.000000000000000225 = 0.000000003000000225
0.000000000000000225 + 0.00000003x + x2 = 0.000000003000000225

Factor a perfect square on the left side:
(x + 0.000000015)(x + 0.000000015) = 0.000000003000000225

Calculate the square root of the right side: 0.000054772

Break this problem into two subproblems by setting 
(x + 0.000000015) equal to 0.000054772 and -0.000054772.


Subproblem 1
x + 0.000000015 = 0.000054772

Simplifying
x + 0.000000015 = 0.000054772

Reorder the terms:
0.000000015 + x = 0.000054772

Solving
0.000000015 + x = 0.000054772

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 = 0.000054772 + -0.000000015

Combine like terms: 0.000000015 + -0.000000015 = 0.000000000
0.000000000 + x = 0.000054772 + -0.000000015
x = 0.000054772 + -0.000000015

Combine like terms: 0.000054772 + -0.000000015 = 0.000054757
x = 0.000054757

Simplifying
x = 0.000054757


Subproblem 2
x + 0.000000015 = -0.000054772

Simplifying
x + 0.000000015 = -0.000054772

Reorder the terms:
0.000000015 + x = -0.000054772

Solving
0.000000015 + x = -0.000054772

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 = -0.000054772 + -0.000000015

Combine like terms: 0.000000015 + -0.000000015 = 0.000000000
0.000000000 + x = -0.000054772 + -0.000000015
x = -0.000054772 + -0.000000015

Combine like terms: -0.000054772 + -0.000000015 = -0.000054787
x = -0.000054787

Simplifying
x = -0.000054787


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.000054757, -0.000054787}

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