0.2x^2-0.16x-0.1=0

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Solution for 0.2x^2-0.16x-0.1=0 equation: 


Simplifying
0.2x2 + -0.16x + -0.1 = 0

Reorder the terms:
-0.1 + -0.16x + 0.2x2 = 0

Solving
-0.1 + -0.16x + 0.2x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
0.2 the coefficient of the squared term: 

Divide each side by '0.2'.
-0.5 + -0.8x + x2 = 0

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + -0.8x + 0.5 + x2 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + -0.8x + x2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + -0.8x + x2 = 0 + 0.5
-0.8x + x2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
-0.8x + x2 = 0.5

The x term is -0.8x.  Take half its coefficient (-0.4).
Square it (0.16) and add it to both sides.

Add '0.16' to each side of the equation.
-0.8x + 0.16 + x2 = 0.5 + 0.16

Reorder the terms:
0.16 + -0.8x + x2 = 0.5 + 0.16

Combine like terms: 0.5 + 0.16 = 0.66
0.16 + -0.8x + x2 = 0.66

Factor a perfect square on the left side:
(x + -0.4)(x + -0.4) = 0.66

Calculate the square root of the right side: 0.81240384

Break this problem into two subproblems by setting 
(x + -0.4) equal to 0.81240384 and -0.81240384.


Subproblem 1
x + -0.4 = 0.81240384

Simplifying
x + -0.4 = 0.81240384

Reorder the terms:
-0.4 + x = 0.81240384

Solving
-0.4 + x = 0.81240384

Solving for variable 'x'.

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

Add '0.4' to each side of the equation.
-0.4 + 0.4 + x = 0.81240384 + 0.4

Combine like terms: -0.4 + 0.4 = 0.0
0.0 + x = 0.81240384 + 0.4
x = 0.81240384 + 0.4

Combine like terms: 0.81240384 + 0.4 = 1.21240384
x = 1.21240384

Simplifying
x = 1.21240384


Subproblem 2
x + -0.4 = -0.81240384

Simplifying
x + -0.4 = -0.81240384

Reorder the terms:
-0.4 + x = -0.81240384

Solving
-0.4 + x = -0.81240384

Solving for variable 'x'.

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

Add '0.4' to each side of the equation.
-0.4 + 0.4 + x = -0.81240384 + 0.4

Combine like terms: -0.4 + 0.4 = 0.0
0.0 + x = -0.81240384 + 0.4
x = -0.81240384 + 0.4

Combine like terms: -0.81240384 + 0.4 = -0.41240384
x = -0.41240384

Simplifying
x = -0.41240384


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.21240384, -0.41240384}

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