0.2x^2+0.31x-0.15=0

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Solution for 0.2x^2+0.31x-0.15=0 equation: 


Simplifying
0.2x2 + 0.31x + -0.15 = 0

Reorder the terms:
-0.15 + 0.31x + 0.2x2 = 0

Solving
-0.15 + 0.31x + 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'.
-0.75 + 1.55x + x2 = 0

Move the constant term to the right:

Add '0.75' to each side of the equation.
-0.75 + 1.55x + 0.75 + x2 = 0 + 0.75

Reorder the terms:
-0.75 + 0.75 + 1.55x + x2 = 0 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + 1.55x + x2 = 0 + 0.75
1.55x + x2 = 0 + 0.75

Combine like terms: 0 + 0.75 = 0.75
1.55x + x2 = 0.75

The x term is 1.55x.  Take half its coefficient (0.775).
Square it (0.600625) and add it to both sides.

Add '0.600625' to each side of the equation.
1.55x + 0.600625 + x2 = 0.75 + 0.600625

Reorder the terms:
0.600625 + 1.55x + x2 = 0.75 + 0.600625

Combine like terms: 0.75 + 0.600625 = 1.350625
0.600625 + 1.55x + x2 = 1.350625

Factor a perfect square on the left side:
(x + 0.775)(x + 0.775) = 1.350625

Calculate the square root of the right side: 1.16216393

Break this problem into two subproblems by setting 
(x + 0.775) equal to 1.16216393 and -1.16216393.


Subproblem 1
x + 0.775 = 1.16216393

Simplifying
x + 0.775 = 1.16216393

Reorder the terms:
0.775 + x = 1.16216393

Solving
0.775 + x = 1.16216393

Solving for variable 'x'.

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

Add '-0.775' to each side of the equation.
0.775 + -0.775 + x = 1.16216393 + -0.775

Combine like terms: 0.775 + -0.775 = 0.000
0.000 + x = 1.16216393 + -0.775
x = 1.16216393 + -0.775

Combine like terms: 1.16216393 + -0.775 = 0.38716393
x = 0.38716393

Simplifying
x = 0.38716393


Subproblem 2
x + 0.775 = -1.16216393

Simplifying
x + 0.775 = -1.16216393

Reorder the terms:
0.775 + x = -1.16216393

Solving
0.775 + x = -1.16216393

Solving for variable 'x'.

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

Add '-0.775' to each side of the equation.
0.775 + -0.775 + x = -1.16216393 + -0.775

Combine like terms: 0.775 + -0.775 = 0.000
0.000 + x = -1.16216393 + -0.775
x = -1.16216393 + -0.775

Combine like terms: -1.16216393 + -0.775 = -1.93716393
x = -1.93716393

Simplifying
x = -1.93716393


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.38716393, -1.93716393}

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