-0.3x^2+0.1x=-0.03

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Solution for -0.3x^2+0.1x=-0.03 equation: 


Simplifying
-0.3x2 + 0.1x = -0.03

Reorder the terms:
0.1x + -0.3x2 = -0.03

Solving
0.1x + -0.3x2 = -0.03

Solving for variable 'x'.

Reorder the terms:
0.03 + 0.1x + -0.3x2 = -0.03 + 0.03

Combine like terms: -0.03 + 0.03 = 0.00
0.03 + 0.1x + -0.3x2 = 0.00

Begin completing the square.  Divide all terms by
-0.3 the coefficient of the squared term: 

Divide each side by '-0.3'.
-0.1 + -0.3333333333x + x2 = 0.0

Move the constant term to the right:

Add '0.1' to each side of the equation.
-0.1 + -0.3333333333x + 0.1 + x2 = 0.0 + 0.1

Reorder the terms:
-0.1 + 0.1 + -0.3333333333x + x2 = 0.0 + 0.1

Combine like terms: -0.1 + 0.1 = 0.0
0.0 + -0.3333333333x + x2 = 0.0 + 0.1
-0.3333333333x + x2 = 0.0 + 0.1

Combine like terms: 0.0 + 0.1 = 0.1
-0.3333333333x + x2 = 0.1

The x term is -0.3333333333x.  Take half its coefficient (-0.1666666667).
Square it (0.02777777779) and add it to both sides.

Add '0.02777777779' to each side of the equation.
-0.3333333333x + 0.02777777779 + x2 = 0.1 + 0.02777777779

Reorder the terms:
0.02777777779 + -0.3333333333x + x2 = 0.1 + 0.02777777779

Combine like terms: 0.1 + 0.02777777779 = 0.12777777779
0.02777777779 + -0.3333333333x + x2 = 0.12777777779

Factor a perfect square on the left side:
(x + -0.1666666667)(x + -0.1666666667) = 0.12777777779

Calculate the square root of the right side: 0.357460177

Break this problem into two subproblems by setting 
(x + -0.1666666667) equal to 0.357460177 and -0.357460177.


Subproblem 1
x + -0.1666666667 = 0.357460177

Simplifying
x + -0.1666666667 = 0.357460177

Reorder the terms:
-0.1666666667 + x = 0.357460177

Solving
-0.1666666667 + x = 0.357460177

Solving for variable 'x'.

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

Add '0.1666666667' to each side of the equation.
-0.1666666667 + 0.1666666667 + x = 0.357460177 + 0.1666666667

Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000
0.0000000000 + x = 0.357460177 + 0.1666666667
x = 0.357460177 + 0.1666666667

Combine like terms: 0.357460177 + 0.1666666667 = 0.5241268437
x = 0.5241268437

Simplifying
x = 0.5241268437


Subproblem 2
x + -0.1666666667 = -0.357460177

Simplifying
x + -0.1666666667 = -0.357460177

Reorder the terms:
-0.1666666667 + x = -0.357460177

Solving
-0.1666666667 + x = -0.357460177

Solving for variable 'x'.

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

Add '0.1666666667' to each side of the equation.
-0.1666666667 + 0.1666666667 + x = -0.357460177 + 0.1666666667

Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000
0.0000000000 + x = -0.357460177 + 0.1666666667
x = -0.357460177 + 0.1666666667

Combine like terms: -0.357460177 + 0.1666666667 = -0.1907935103
x = -0.1907935103

Simplifying
x = -0.1907935103


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.5241268437, -0.1907935103}

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