(x^2)+(.133x)-0.036=0

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Solution for (x^2)+(.133x)-0.036=0 equation: 


Simplifying
(x2) + (0.133x) + -0.036 = 0
x2 + (0.133x) + -0.036 = 0

Reorder the terms:
-0.036 + (0.133x) + x2 = 0

Solving
-0.036 + (0.133x) + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '0.036' to each side of the equation.
-0.036 + (0.133x) + 0.036 + x2 = 0 + 0.036

Reorder the terms:
-0.036 + 0.036 + (0.133x) + x2 = 0 + 0.036

Combine like terms: -0.036 + 0.036 = 0.000
0.000 + (0.133x) + x2 = 0 + 0.036
(0.133x) + x2 = 0 + 0.036

Combine like terms: 0 + 0.036 = 0.036
(0.133x) + x2 = 0.036

The x term is (0.133x).  Take half its coefficient (0.0665).
Square it (0.00442225) and add it to both sides.

Add '0.00442225' to each side of the equation.
(0.133x) + 0.00442225 + x2 = 0.036 + 0.00442225

Reorder the terms:
0.00442225 + (0.133x) + x2 = 0.036 + 0.00442225

Combine like terms: 0.036 + 0.00442225 = 0.04042225
0.00442225 + (0.133x) + x2 = 0.04042225

Factor a perfect square on the left side:
(x + 0.0665)(x + 0.0665) = 0.04042225

Calculate the square root of the right side: 0.201052854

Break this problem into two subproblems by setting 
(x + 0.0665) equal to 0.201052854 and -0.201052854.


Subproblem 1
x + 0.0665 = 0.201052854

Simplifying
x + 0.0665 = 0.201052854

Reorder the terms:
0.0665 + x = 0.201052854

Solving
0.0665 + x = 0.201052854

Solving for variable 'x'.

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

Add '-0.0665' to each side of the equation.
0.0665 + -0.0665 + x = 0.201052854 + -0.0665

Combine like terms: 0.0665 + -0.0665 = 0.0000
0.0000 + x = 0.201052854 + -0.0665
x = 0.201052854 + -0.0665

Combine like terms: 0.201052854 + -0.0665 = 0.134552854
x = 0.134552854

Simplifying
x = 0.134552854


Subproblem 2
x + 0.0665 = -0.201052854

Simplifying
x + 0.0665 = -0.201052854

Reorder the terms:
0.0665 + x = -0.201052854

Solving
0.0665 + x = -0.201052854

Solving for variable 'x'.

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

Add '-0.0665' to each side of the equation.
0.0665 + -0.0665 + x = -0.201052854 + -0.0665

Combine like terms: 0.0665 + -0.0665 = 0.0000
0.0000 + x = -0.201052854 + -0.0665
x = -0.201052854 + -0.0665

Combine like terms: -0.201052854 + -0.0665 = -0.267552854
x = -0.267552854

Simplifying
x = -0.267552854


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.134552854, -0.267552854}

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