x^2+.05x-(.00000003)=0

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Solution for x^2+.05x-(.00000003)=0 equation: 


Simplifying
x2 + 0.05x + -1(0.00000003) = 0

Multiply -1 * 0.00000003
x2 + 0.05x + -0.00000003 = 0

Reorder the terms:
-0.00000003 + 0.05x + x2 = 0

Solving
-0.00000003 + 0.05x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '0.00000003' to each side of the equation.
-0.00000003 + 0.05x + 0.00000003 + x2 = 0 + 0.00000003

Reorder the terms:
-0.00000003 + 0.00000003 + 0.05x + x2 = 0 + 0.00000003

Combine like terms: -0.00000003 + 0.00000003 = 0.00000000
0.00000000 + 0.05x + x2 = 0 + 0.00000003
0.05x + x2 = 0 + 0.00000003

Combine like terms: 0 + 0.00000003 = 0.00000003
0.05x + x2 = 0.00000003

The x term is 0.05x.  Take half its coefficient (0.025).
Square it (0.000625) and add it to both sides.

Add '0.000625' to each side of the equation.
0.05x + 0.000625 + x2 = 0.00000003 + 0.000625

Reorder the terms:
0.000625 + 0.05x + x2 = 0.00000003 + 0.000625

Combine like terms: 0.00000003 + 0.000625 = 0.00062503
0.000625 + 0.05x + x2 = 0.00062503

Factor a perfect square on the left side:
(x + 0.025)(x + 0.025) = 0.00062503

Calculate the square root of the right side: 0.0250006

Break this problem into two subproblems by setting 
(x + 0.025) equal to 0.0250006 and -0.0250006.


Subproblem 1
x + 0.025 = 0.0250006

Simplifying
x + 0.025 = 0.0250006

Reorder the terms:
0.025 + x = 0.0250006

Solving
0.025 + x = 0.0250006

Solving for variable 'x'.

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

Add '-0.025' to each side of the equation.
0.025 + -0.025 + x = 0.0250006 + -0.025

Combine like terms: 0.025 + -0.025 = 0.000
0.000 + x = 0.0250006 + -0.025
x = 0.0250006 + -0.025

Combine like terms: 0.0250006 + -0.025 = 0.0000006
x = 0.0000006

Simplifying
x = 0.0000006


Subproblem 2
x + 0.025 = -0.0250006

Simplifying
x + 0.025 = -0.0250006

Reorder the terms:
0.025 + x = -0.0250006

Solving
0.025 + x = -0.0250006

Solving for variable 'x'.

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

Add '-0.025' to each side of the equation.
0.025 + -0.025 + x = -0.0250006 + -0.025

Combine like terms: 0.025 + -0.025 = 0.000
0.000 + x = -0.0250006 + -0.025
x = -0.0250006 + -0.025

Combine like terms: -0.0250006 + -0.025 = -0.0500006
x = -0.0500006

Simplifying
x = -0.0500006


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.0000006, -0.0500006}

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