x^2+0.1x-0.66=0

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Solution for x^2+0.1x-0.66=0 equation: 


Simplifying
x2 + 0.1x + -0.66 = 0

Reorder the terms:
-0.66 + 0.1x + x2 = 0

Solving
-0.66 + 0.1x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '0.66' to each side of the equation.
-0.66 + 0.1x + 0.66 + x2 = 0 + 0.66

Reorder the terms:
-0.66 + 0.66 + 0.1x + x2 = 0 + 0.66

Combine like terms: -0.66 + 0.66 = 0.00
0.00 + 0.1x + x2 = 0 + 0.66
0.1x + x2 = 0 + 0.66

Combine like terms: 0 + 0.66 = 0.66
0.1x + x2 = 0.66

The x term is 0.1x.  Take half its coefficient (0.05).
Square it (0.0025) and add it to both sides.

Add '0.0025' to each side of the equation.
0.1x + 0.0025 + x2 = 0.66 + 0.0025

Reorder the terms:
0.0025 + 0.1x + x2 = 0.66 + 0.0025

Combine like terms: 0.66 + 0.0025 = 0.6625
0.0025 + 0.1x + x2 = 0.6625

Factor a perfect square on the left side:
(x + 0.05)(x + 0.05) = 0.6625

Calculate the square root of the right side: 0.81394103

Break this problem into two subproblems by setting 
(x + 0.05) equal to 0.81394103 and -0.81394103.


Subproblem 1
x + 0.05 = 0.81394103

Simplifying
x + 0.05 = 0.81394103

Reorder the terms:
0.05 + x = 0.81394103

Solving
0.05 + x = 0.81394103

Solving for variable 'x'.

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

Add '-0.05' to each side of the equation.
0.05 + -0.05 + x = 0.81394103 + -0.05

Combine like terms: 0.05 + -0.05 = 0.00
0.00 + x = 0.81394103 + -0.05
x = 0.81394103 + -0.05

Combine like terms: 0.81394103 + -0.05 = 0.76394103
x = 0.76394103

Simplifying
x = 0.76394103


Subproblem 2
x + 0.05 = -0.81394103

Simplifying
x + 0.05 = -0.81394103

Reorder the terms:
0.05 + x = -0.81394103

Solving
0.05 + x = -0.81394103

Solving for variable 'x'.

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

Add '-0.05' to each side of the equation.
0.05 + -0.05 + x = -0.81394103 + -0.05

Combine like terms: 0.05 + -0.05 = 0.00
0.00 + x = -0.81394103 + -0.05
x = -0.81394103 + -0.05

Combine like terms: -0.81394103 + -0.05 = -0.86394103
x = -0.86394103

Simplifying
x = -0.86394103


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.76394103, -0.86394103}

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