3x^2-46x-33=0

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Solution for 3x^2-46x-33=0 equation: 


Simplifying
3x2 + -46x + -33 = 0

Reorder the terms:
-33 + -46x + 3x2 = 0

Solving
-33 + -46x + 3x2 = 0

Solving for variable 'x'.

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

Divide each side by '3'.
-11 + -15.33333333x + x2 = 0

Move the constant term to the right:

Add '11' to each side of the equation.
-11 + -15.33333333x + 11 + x2 = 0 + 11

Reorder the terms:
-11 + 11 + -15.33333333x + x2 = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -15.33333333x + x2 = 0 + 11
-15.33333333x + x2 = 0 + 11

Combine like terms: 0 + 11 = 11
-15.33333333x + x2 = 11

The x term is -15.33333333x.  Take half its coefficient (-7.666666665).
Square it (58.77777775) and add it to both sides.

Add '58.77777775' to each side of the equation.
-15.33333333x + 58.77777775 + x2 = 11 + 58.77777775

Reorder the terms:
58.77777775 + -15.33333333x + x2 = 11 + 58.77777775

Combine like terms: 11 + 58.77777775 = 69.77777775
58.77777775 + -15.33333333x + x2 = 69.77777775

Factor a perfect square on the left side:
(x + -7.666666665)(x + -7.666666665) = 69.77777775

Calculate the square root of the right side: 8.353309389

Break this problem into two subproblems by setting 
(x + -7.666666665) equal to 8.353309389 and -8.353309389.


Subproblem 1
x + -7.666666665 = 8.353309389

Simplifying
x + -7.666666665 = 8.353309389

Reorder the terms:
-7.666666665 + x = 8.353309389

Solving
-7.666666665 + x = 8.353309389

Solving for variable 'x'.

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

Add '7.666666665' to each side of the equation.
-7.666666665 + 7.666666665 + x = 8.353309389 + 7.666666665

Combine like terms: -7.666666665 + 7.666666665 = 0.000000000
0.000000000 + x = 8.353309389 + 7.666666665
x = 8.353309389 + 7.666666665

Combine like terms: 8.353309389 + 7.666666665 = 16.019976054
x = 16.019976054

Simplifying
x = 16.019976054


Subproblem 2
x + -7.666666665 = -8.353309389

Simplifying
x + -7.666666665 = -8.353309389

Reorder the terms:
-7.666666665 + x = -8.353309389

Solving
-7.666666665 + x = -8.353309389

Solving for variable 'x'.

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

Add '7.666666665' to each side of the equation.
-7.666666665 + 7.666666665 + x = -8.353309389 + 7.666666665

Combine like terms: -7.666666665 + 7.666666665 = 0.000000000
0.000000000 + x = -8.353309389 + 7.666666665
x = -8.353309389 + 7.666666665

Combine like terms: -8.353309389 + 7.666666665 = -0.686642724
x = -0.686642724

Simplifying
x = -0.686642724


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {16.019976054, -0.686642724}

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