-0.0316+0.0395x+0.9921x^2=0

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Solution for -0.0316+0.0395x+0.9921x^2=0 equation: 


Simplifying
-0.0316 + 0.0395x + 0.9921x2 = 0

Solving
-0.0316 + 0.0395x + 0.9921x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
0.9921 the coefficient of the squared term: 

Divide each side by '0.9921'.
-0.03185162786 + 0.03981453483x + x2 = 0

Move the constant term to the right:

Add '0.03185162786' to each side of the equation.
-0.03185162786 + 0.03981453483x + 0.03185162786 + x2 = 0 + 0.03185162786

Reorder the terms:
-0.03185162786 + 0.03185162786 + 0.03981453483x + x2 = 0 + 0.03185162786

Combine like terms: -0.03185162786 + 0.03185162786 = 0.00000000000
0.00000000000 + 0.03981453483x + x2 = 0 + 0.03185162786
0.03981453483x + x2 = 0 + 0.03185162786

Combine like terms: 0 + 0.03185162786 = 0.03185162786
0.03981453483x + x2 = 0.03185162786

The x term is 0.03981453483x.  Take half its coefficient (0.01990726742).
Square it (0.0003962992961) and add it to both sides.

Add '0.0003962992961' to each side of the equation.
0.03981453483x + 0.0003962992961 + x2 = 0.03185162786 + 0.0003962992961

Reorder the terms:
0.0003962992961 + 0.03981453483x + x2 = 0.03185162786 + 0.0003962992961

Combine like terms: 0.03185162786 + 0.0003962992961 = 0.0322479271561
0.0003962992961 + 0.03981453483x + x2 = 0.0322479271561

Factor a perfect square on the left side:
(x + 0.01990726742)(x + 0.01990726742) = 0.0322479271561

Calculate the square root of the right side: 0.179577079

Break this problem into two subproblems by setting 
(x + 0.01990726742) equal to 0.179577079 and -0.179577079.


Subproblem 1
x + 0.01990726742 = 0.179577079

Simplifying
x + 0.01990726742 = 0.179577079

Reorder the terms:
0.01990726742 + x = 0.179577079

Solving
0.01990726742 + x = 0.179577079

Solving for variable 'x'.

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

Add '-0.01990726742' to each side of the equation.
0.01990726742 + -0.01990726742 + x = 0.179577079 + -0.01990726742

Combine like terms: 0.01990726742 + -0.01990726742 = 0.00000000000
0.00000000000 + x = 0.179577079 + -0.01990726742
x = 0.179577079 + -0.01990726742

Combine like terms: 0.179577079 + -0.01990726742 = 0.15966981158
x = 0.15966981158

Simplifying
x = 0.15966981158


Subproblem 2
x + 0.01990726742 = -0.179577079

Simplifying
x + 0.01990726742 = -0.179577079

Reorder the terms:
0.01990726742 + x = -0.179577079

Solving
0.01990726742 + x = -0.179577079

Solving for variable 'x'.

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

Add '-0.01990726742' to each side of the equation.
0.01990726742 + -0.01990726742 + x = -0.179577079 + -0.01990726742

Combine like terms: 0.01990726742 + -0.01990726742 = 0.00000000000
0.00000000000 + x = -0.179577079 + -0.01990726742
x = -0.179577079 + -0.01990726742

Combine like terms: -0.179577079 + -0.01990726742 = -0.19948434642
x = -0.19948434642

Simplifying
x = -0.19948434642


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.15966981158, -0.19948434642}

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