-3x=.333333x^2+6

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Solution for -3x=.333333x^2+6 equation:


Simplifying
-3x = 0.333333x2 + 6

Reorder the terms:
-3x = 6 + 0.333333x2

Solving
-3x = 6 + 0.333333x2

Solving for variable 'x'.

Reorder the terms:
-6 + -3x + -0.333333x2 = 6 + 0.333333x2 + -6 + -0.333333x2

Reorder the terms:
-6 + -3x + -0.333333x2 = 6 + -6 + 0.333333x2 + -0.333333x2

Combine like terms: 6 + -6 = 0
-6 + -3x + -0.333333x2 = 0 + 0.333333x2 + -0.333333x2
-6 + -3x + -0.333333x2 = 0.333333x2 + -0.333333x2

Combine like terms: 0.333333x2 + -0.333333x2 = 0.000000
-6 + -3x + -0.333333x2 = 0.000000

Begin completing the square.  Divide all terms by
-0.333333 the coefficient of the squared term: 

Divide each side by '-0.333333'.
18.000018 + 9.000009x + x2 = 0

Move the constant term to the right:

Add '-18.000018' to each side of the equation.
18.000018 + 9.000009x + -18.000018 + x2 = 0 + -18.000018

Reorder the terms:
18.000018 + -18.000018 + 9.000009x + x2 = 0 + -18.000018

Combine like terms: 18.000018 + -18.000018 = 0.000000
0.000000 + 9.000009x + x2 = 0 + -18.000018
9.000009x + x2 = 0 + -18.000018

Combine like terms: 0 + -18.000018 = -18.000018
9.000009x + x2 = -18.000018

The x term is 9.000009x.  Take half its coefficient (4.5000045).
Square it (20.25004050) and add it to both sides.

Add '20.25004050' to each side of the equation.
9.000009x + 20.25004050 + x2 = -18.000018 + 20.25004050

Reorder the terms:
20.25004050 + 9.000009x + x2 = -18.000018 + 20.25004050

Combine like terms: -18.000018 + 20.25004050 = 2.2500225
20.25004050 + 9.000009x + x2 = 2.2500225

Factor a perfect square on the left side:
(x + 4.5000045)(x + 4.5000045) = 2.2500225

Calculate the square root of the right side: 1.5000075

Break this problem into two subproblems by setting 
(x + 4.5000045) equal to 1.5000075 and -1.5000075.

Subproblem 1

x + 4.5000045 = 1.5000075 Simplifying x + 4.5000045 = 1.5000075 Reorder the terms: 4.5000045 + x = 1.5000075 Solving 4.5000045 + x = 1.5000075 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5000045' to each side of the equation. 4.5000045 + -4.5000045 + x = 1.5000075 + -4.5000045 Combine like terms: 4.5000045 + -4.5000045 = 0.0000000 0.0000000 + x = 1.5000075 + -4.5000045 x = 1.5000075 + -4.5000045 Combine like terms: 1.5000075 + -4.5000045 = -2.999997 x = -2.999997 Simplifying x = -2.999997

Subproblem 2

x + 4.5000045 = -1.5000075 Simplifying x + 4.5000045 = -1.5000075 Reorder the terms: 4.5000045 + x = -1.5000075 Solving 4.5000045 + x = -1.5000075 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5000045' to each side of the equation. 4.5000045 + -4.5000045 + x = -1.5000075 + -4.5000045 Combine like terms: 4.5000045 + -4.5000045 = 0.0000000 0.0000000 + x = -1.5000075 + -4.5000045 x = -1.5000075 + -4.5000045 Combine like terms: -1.5000075 + -4.5000045 = -6.000012 x = -6.000012 Simplifying x = -6.000012

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-2.999997, -6.000012}

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