x^2+0.0201x-0.0078591=0

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Solution for x^2+0.0201x-0.0078591=0 equation: 


Simplifying
x2 + 0.0201x + -0.0078591 = 0

Reorder the terms:
-0.0078591 + 0.0201x + x2 = 0

Solving
-0.0078591 + 0.0201x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '0.0078591' to each side of the equation.
-0.0078591 + 0.0201x + 0.0078591 + x2 = 0 + 0.0078591

Reorder the terms:
-0.0078591 + 0.0078591 + 0.0201x + x2 = 0 + 0.0078591

Combine like terms: -0.0078591 + 0.0078591 = 0.0000000
0.0000000 + 0.0201x + x2 = 0 + 0.0078591
0.0201x + x2 = 0 + 0.0078591

Combine like terms: 0 + 0.0078591 = 0.0078591
0.0201x + x2 = 0.0078591

The x term is 0.0201x.  Take half its coefficient (0.01005).
Square it (0.0001010025) and add it to both sides.

Add '0.0001010025' to each side of the equation.
0.0201x + 0.0001010025 + x2 = 0.0078591 + 0.0001010025

Reorder the terms:
0.0001010025 + 0.0201x + x2 = 0.0078591 + 0.0001010025

Combine like terms: 0.0078591 + 0.0001010025 = 0.0079601025
0.0001010025 + 0.0201x + x2 = 0.0079601025

Factor a perfect square on the left side:
(x + 0.01005)(x + 0.01005) = 0.0079601025

Calculate the square root of the right side: 0.089219407

Break this problem into two subproblems by setting 
(x + 0.01005) equal to 0.089219407 and -0.089219407.


Subproblem 1
x + 0.01005 = 0.089219407

Simplifying
x + 0.01005 = 0.089219407

Reorder the terms:
0.01005 + x = 0.089219407

Solving
0.01005 + x = 0.089219407

Solving for variable 'x'.

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

Add '-0.01005' to each side of the equation.
0.01005 + -0.01005 + x = 0.089219407 + -0.01005

Combine like terms: 0.01005 + -0.01005 = 0.00000
0.00000 + x = 0.089219407 + -0.01005
x = 0.089219407 + -0.01005

Combine like terms: 0.089219407 + -0.01005 = 0.079169407
x = 0.079169407

Simplifying
x = 0.079169407


Subproblem 2
x + 0.01005 = -0.089219407

Simplifying
x + 0.01005 = -0.089219407

Reorder the terms:
0.01005 + x = -0.089219407

Solving
0.01005 + x = -0.089219407

Solving for variable 'x'.

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

Add '-0.01005' to each side of the equation.
0.01005 + -0.01005 + x = -0.089219407 + -0.01005

Combine like terms: 0.01005 + -0.01005 = 0.00000
0.00000 + x = -0.089219407 + -0.01005
x = -0.089219407 + -0.01005

Combine like terms: -0.089219407 + -0.01005 = -0.099269407
x = -0.099269407

Simplifying
x = -0.099269407


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.079169407, -0.099269407}

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