x^2+.3333x=31.8309

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Solution for x^2+.3333x=31.8309 equation: 


Simplifying
x2 + 0.3333x = 31.8309

Reorder the terms:
0.3333x + x2 = 31.8309

Solving
0.3333x + x2 = 31.8309

Solving for variable 'x'.

Reorder the terms:
-31.8309 + 0.3333x + x2 = 31.8309 + -31.8309

Combine like terms: 31.8309 + -31.8309 = 0.0000
-31.8309 + 0.3333x + x2 = 0.0000

Begin completing the square.

Move the constant term to the right:

Add '31.8309' to each side of the equation.
-31.8309 + 0.3333x + 31.8309 + x2 = 0.0000 + 31.8309

Reorder the terms:
-31.8309 + 31.8309 + 0.3333x + x2 = 0.0000 + 31.8309

Combine like terms: -31.8309 + 31.8309 = 0.0000
0.0000 + 0.3333x + x2 = 0.0000 + 31.8309
0.3333x + x2 = 0.0000 + 31.8309

Combine like terms: 0.0000 + 31.8309 = 31.8309
0.3333x + x2 = 31.8309

The x term is 0.3333x.  Take half its coefficient (0.16665).
Square it (0.0277722225) and add it to both sides.

Add '0.0277722225' to each side of the equation.
0.3333x + 0.0277722225 + x2 = 31.8309 + 0.0277722225

Reorder the terms:
0.0277722225 + 0.3333x + x2 = 31.8309 + 0.0277722225

Combine like terms: 31.8309 + 0.0277722225 = 31.8586722225
0.0277722225 + 0.3333x + x2 = 31.8586722225

Factor a perfect square on the left side:
(x + 0.16665)(x + 0.16665) = 31.8586722225

Calculate the square root of the right side: 5.644348698

Break this problem into two subproblems by setting 
(x + 0.16665) equal to 5.644348698 and -5.644348698.


Subproblem 1
x + 0.16665 = 5.644348698

Simplifying
x + 0.16665 = 5.644348698

Reorder the terms:
0.16665 + x = 5.644348698

Solving
0.16665 + x = 5.644348698

Solving for variable 'x'.

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

Add '-0.16665' to each side of the equation.
0.16665 + -0.16665 + x = 5.644348698 + -0.16665

Combine like terms: 0.16665 + -0.16665 = 0.00000
0.00000 + x = 5.644348698 + -0.16665
x = 5.644348698 + -0.16665

Combine like terms: 5.644348698 + -0.16665 = 5.477698698
x = 5.477698698

Simplifying
x = 5.477698698


Subproblem 2
x + 0.16665 = -5.644348698

Simplifying
x + 0.16665 = -5.644348698

Reorder the terms:
0.16665 + x = -5.644348698

Solving
0.16665 + x = -5.644348698

Solving for variable 'x'.

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

Add '-0.16665' to each side of the equation.
0.16665 + -0.16665 + x = -5.644348698 + -0.16665

Combine like terms: 0.16665 + -0.16665 = 0.00000
0.00000 + x = -5.644348698 + -0.16665
x = -5.644348698 + -0.16665

Combine like terms: -5.644348698 + -0.16665 = -5.810998698
x = -5.810998698

Simplifying
x = -5.810998698


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.477698698, -5.810998698}

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