330=3x^2+2x+6

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Solution for 330=3x^2+2x+6 equation:


Simplifying
330 = 3x2 + 2x + 6

Reorder the terms:
330 = 6 + 2x + 3x2

Solving
330 = 6 + 2x + 3x2

Solving for variable 'x'.

Combine like terms: 330 + -6 = 324
324 + -2x + -3x2 = 6 + 2x + 3x2 + -6 + -2x + -3x2

Reorder the terms:
324 + -2x + -3x2 = 6 + -6 + 2x + -2x + 3x2 + -3x2

Combine like terms: 6 + -6 = 0
324 + -2x + -3x2 = 0 + 2x + -2x + 3x2 + -3x2
324 + -2x + -3x2 = 2x + -2x + 3x2 + -3x2

Combine like terms: 2x + -2x = 0
324 + -2x + -3x2 = 0 + 3x2 + -3x2
324 + -2x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
324 + -2x + -3x2 = 0

Begin completing the square.  Divide all terms by
-3 the coefficient of the squared term: 

Divide each side by '-3'.
-108 + 0.6666666667x + x2 = 0

Move the constant term to the right:

Add '108' to each side of the equation.
-108 + 0.6666666667x + 108 + x2 = 0 + 108

Reorder the terms:
-108 + 108 + 0.6666666667x + x2 = 0 + 108

Combine like terms: -108 + 108 = 0
0 + 0.6666666667x + x2 = 0 + 108
0.6666666667x + x2 = 0 + 108

Combine like terms: 0 + 108 = 108
0.6666666667x + x2 = 108

The x term is 0.6666666667x.  Take half its coefficient (0.3333333334).
Square it (0.1111111112) and add it to both sides.

Add '0.1111111112' to each side of the equation.
0.6666666667x + 0.1111111112 + x2 = 108 + 0.1111111112

Reorder the terms:
0.1111111112 + 0.6666666667x + x2 = 108 + 0.1111111112

Combine like terms: 108 + 0.1111111112 = 108.1111111112
0.1111111112 + 0.6666666667x + x2 = 108.1111111112

Factor a perfect square on the left side:
(x + 0.3333333334)(x + 0.3333333334) = 108.1111111112

Calculate the square root of the right side: 10.397649307

Break this problem into two subproblems by setting 
(x + 0.3333333334) equal to 10.397649307 and -10.397649307.

Subproblem 1

x + 0.3333333334 = 10.397649307 Simplifying x + 0.3333333334 = 10.397649307 Reorder the terms: 0.3333333334 + x = 10.397649307 Solving 0.3333333334 + x = 10.397649307 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + x = 10.397649307 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = 10.397649307 + -0.3333333334 x = 10.397649307 + -0.3333333334 Combine like terms: 10.397649307 + -0.3333333334 = 10.0643159736 x = 10.0643159736 Simplifying x = 10.0643159736

Subproblem 2

x + 0.3333333334 = -10.397649307 Simplifying x + 0.3333333334 = -10.397649307 Reorder the terms: 0.3333333334 + x = -10.397649307 Solving 0.3333333334 + x = -10.397649307 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + x = -10.397649307 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = -10.397649307 + -0.3333333334 x = -10.397649307 + -0.3333333334 Combine like terms: -10.397649307 + -0.3333333334 = -10.7309826404 x = -10.7309826404 Simplifying x = -10.7309826404

Solution

The solution to the problem is based on the solutions from the subproblems. x = {10.0643159736, -10.7309826404}

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