x^2+0.0000045x-0.000001035=0

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Solution for x^2+0.0000045x-0.000001035=0 equation: 


Simplifying
x2 + 0.0000045x + -0.000001035 = 0

Reorder the terms:
-0.000001035 + 0.0000045x + x2 = 0

Solving
-0.000001035 + 0.0000045x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '0.000001035' to each side of the equation.
-0.000001035 + 0.0000045x + 0.000001035 + x2 = 0 + 0.000001035

Reorder the terms:
-0.000001035 + 0.000001035 + 0.0000045x + x2 = 0 + 0.000001035

Combine like terms: -0.000001035 + 0.000001035 = 0.000000000
0.000000000 + 0.0000045x + x2 = 0 + 0.000001035
0.0000045x + x2 = 0 + 0.000001035

Combine like terms: 0 + 0.000001035 = 0.000001035
0.0000045x + x2 = 0.000001035

The x term is 0.0000045x.  Take half its coefficient (0.00000225).
Square it (0.0000000000050625) and add it to both sides.

Add '0.0000000000050625' to each side of the equation.
0.0000045x + 0.0000000000050625 + x2 = 0.000001035 + 0.0000000000050625

Reorder the terms:
0.0000000000050625 + 0.0000045x + x2 = 0.000001035 + 0.0000000000050625

Combine like terms: 0.000001035 + 0.0000000000050625 = 0.0000010350050625
0.0000000000050625 + 0.0000045x + x2 = 0.0000010350050625

Factor a perfect square on the left side:
(x + 0.00000225)(x + 0.00000225) = 0.0000010350050625

Calculate the square root of the right side: 0.001017352

Break this problem into two subproblems by setting 
(x + 0.00000225) equal to 0.001017352 and -0.001017352.


Subproblem 1
x + 0.00000225 = 0.001017352

Simplifying
x + 0.00000225 = 0.001017352

Reorder the terms:
0.00000225 + x = 0.001017352

Solving
0.00000225 + x = 0.001017352

Solving for variable 'x'.

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

Add '-0.00000225' to each side of the equation.
0.00000225 + -0.00000225 + x = 0.001017352 + -0.00000225

Combine like terms: 0.00000225 + -0.00000225 = 0.00000000
0.00000000 + x = 0.001017352 + -0.00000225
x = 0.001017352 + -0.00000225

Combine like terms: 0.001017352 + -0.00000225 = 0.001015102
x = 0.001015102

Simplifying
x = 0.001015102


Subproblem 2
x + 0.00000225 = -0.001017352

Simplifying
x + 0.00000225 = -0.001017352

Reorder the terms:
0.00000225 + x = -0.001017352

Solving
0.00000225 + x = -0.001017352

Solving for variable 'x'.

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

Add '-0.00000225' to each side of the equation.
0.00000225 + -0.00000225 + x = -0.001017352 + -0.00000225

Combine like terms: 0.00000225 + -0.00000225 = 0.00000000
0.00000000 + x = -0.001017352 + -0.00000225
x = -0.001017352 + -0.00000225

Combine like terms: -0.001017352 + -0.00000225 = -0.001019602
x = -0.001019602

Simplifying
x = -0.001019602


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.001015102, -0.001019602}

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