-0.8x^2-0.36x+0.16=0

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Solution for -0.8x^2-0.36x+0.16=0 equation: 


Simplifying
-0.8x2 + -0.36x + 0.16 = 0

Reorder the terms:
0.16 + -0.36x + -0.8x2 = 0

Solving
0.16 + -0.36x + -0.8x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-0.8 the coefficient of the squared term: 

Divide each side by '-0.8'.
-0.2 + 0.45x + x2 = 0

Move the constant term to the right:

Add '0.2' to each side of the equation.
-0.2 + 0.45x + 0.2 + x2 = 0 + 0.2

Reorder the terms:
-0.2 + 0.2 + 0.45x + x2 = 0 + 0.2

Combine like terms: -0.2 + 0.2 = 0.0
0.0 + 0.45x + x2 = 0 + 0.2
0.45x + x2 = 0 + 0.2

Combine like terms: 0 + 0.2 = 0.2
0.45x + x2 = 0.2

The x term is 0.45x.  Take half its coefficient (0.225).
Square it (0.050625) and add it to both sides.

Add '0.050625' to each side of the equation.
0.45x + 0.050625 + x2 = 0.2 + 0.050625

Reorder the terms:
0.050625 + 0.45x + x2 = 0.2 + 0.050625

Combine like terms: 0.2 + 0.050625 = 0.250625
0.050625 + 0.45x + x2 = 0.250625

Factor a perfect square on the left side:
(x + 0.225)(x + 0.225) = 0.250625

Calculate the square root of the right side: 0.50062461

Break this problem into two subproblems by setting 
(x + 0.225) equal to 0.50062461 and -0.50062461.


Subproblem 1
x + 0.225 = 0.50062461

Simplifying
x + 0.225 = 0.50062461

Reorder the terms:
0.225 + x = 0.50062461

Solving
0.225 + x = 0.50062461

Solving for variable 'x'.

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

Add '-0.225' to each side of the equation.
0.225 + -0.225 + x = 0.50062461 + -0.225

Combine like terms: 0.225 + -0.225 = 0.000
0.000 + x = 0.50062461 + -0.225
x = 0.50062461 + -0.225

Combine like terms: 0.50062461 + -0.225 = 0.27562461
x = 0.27562461

Simplifying
x = 0.27562461


Subproblem 2
x + 0.225 = -0.50062461

Simplifying
x + 0.225 = -0.50062461

Reorder the terms:
0.225 + x = -0.50062461

Solving
0.225 + x = -0.50062461

Solving for variable 'x'.

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

Add '-0.225' to each side of the equation.
0.225 + -0.225 + x = -0.50062461 + -0.225

Combine like terms: 0.225 + -0.225 = 0.000
0.000 + x = -0.50062461 + -0.225
x = -0.50062461 + -0.225

Combine like terms: -0.50062461 + -0.225 = -0.72562461
x = -0.72562461

Simplifying
x = -0.72562461


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.27562461, -0.72562461}

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