3x^2-10x-33=0

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Solution for 3x^2-10x-33=0 equation: 


Simplifying
3x2 + -10x + -33 = 0

Reorder the terms:
-33 + -10x + 3x2 = 0

Solving
-33 + -10x + 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 + -3.333333333x + x2 = 0

Move the constant term to the right:

Add '11' to each side of the equation.
-11 + -3.333333333x + 11 + x2 = 0 + 11

Reorder the terms:
-11 + 11 + -3.333333333x + x2 = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -3.333333333x + x2 = 0 + 11
-3.333333333x + x2 = 0 + 11

Combine like terms: 0 + 11 = 11
-3.333333333x + x2 = 11

The x term is -3.333333333x.  Take half its coefficient (-1.666666667).
Square it (2.777777779) and add it to both sides.

Add '2.777777779' to each side of the equation.
-3.333333333x + 2.777777779 + x2 = 11 + 2.777777779

Reorder the terms:
2.777777779 + -3.333333333x + x2 = 11 + 2.777777779

Combine like terms: 11 + 2.777777779 = 13.777777779
2.777777779 + -3.333333333x + x2 = 13.777777779

Factor a perfect square on the left side:
(x + -1.666666667)(x + -1.666666667) = 13.777777779

Calculate the square root of the right side: 3.711842909

Break this problem into two subproblems by setting 
(x + -1.666666667) equal to 3.711842909 and -3.711842909.


Subproblem 1
x + -1.666666667 = 3.711842909

Simplifying
x + -1.666666667 = 3.711842909

Reorder the terms:
-1.666666667 + x = 3.711842909

Solving
-1.666666667 + x = 3.711842909

Solving for variable 'x'.

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

Add '1.666666667' to each side of the equation.
-1.666666667 + 1.666666667 + x = 3.711842909 + 1.666666667

Combine like terms: -1.666666667 + 1.666666667 = 0.000000000
0.000000000 + x = 3.711842909 + 1.666666667
x = 3.711842909 + 1.666666667

Combine like terms: 3.711842909 + 1.666666667 = 5.378509576
x = 5.378509576

Simplifying
x = 5.378509576


Subproblem 2
x + -1.666666667 = -3.711842909

Simplifying
x + -1.666666667 = -3.711842909

Reorder the terms:
-1.666666667 + x = -3.711842909

Solving
-1.666666667 + x = -3.711842909

Solving for variable 'x'.

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

Add '1.666666667' to each side of the equation.
-1.666666667 + 1.666666667 + x = -3.711842909 + 1.666666667

Combine like terms: -1.666666667 + 1.666666667 = 0.000000000
0.000000000 + x = -3.711842909 + 1.666666667
x = -3.711842909 + 1.666666667

Combine like terms: -3.711842909 + 1.666666667 = -2.045176242
x = -2.045176242

Simplifying
x = -2.045176242


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.378509576, -2.045176242}

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