3x^2-26x-33=0

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Solution for 3x^2-26x-33=0 equation: 


Simplifying
3x2 + -26x + -33 = 0

Reorder the terms:
-33 + -26x + 3x2 = 0

Solving
-33 + -26x + 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 + -8.666666667x + x2 = 0

Move the constant term to the right:

Add '11' to each side of the equation.
-11 + -8.666666667x + 11 + x2 = 0 + 11

Reorder the terms:
-11 + 11 + -8.666666667x + x2 = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -8.666666667x + x2 = 0 + 11
-8.666666667x + x2 = 0 + 11

Combine like terms: 0 + 11 = 11
-8.666666667x + x2 = 11

The x term is -8.666666667x.  Take half its coefficient (-4.333333334).
Square it (18.77777778) and add it to both sides.

Add '18.77777778' to each side of the equation.
-8.666666667x + 18.77777778 + x2 = 11 + 18.77777778

Reorder the terms:
18.77777778 + -8.666666667x + x2 = 11 + 18.77777778

Combine like terms: 11 + 18.77777778 = 29.77777778
18.77777778 + -8.666666667x + x2 = 29.77777778

Factor a perfect square on the left side:
(x + -4.333333334)(x + -4.333333334) = 29.77777778

Calculate the square root of the right side: 5.456901848

Break this problem into two subproblems by setting 
(x + -4.333333334) equal to 5.456901848 and -5.456901848.


Subproblem 1
x + -4.333333334 = 5.456901848

Simplifying
x + -4.333333334 = 5.456901848

Reorder the terms:
-4.333333334 + x = 5.456901848

Solving
-4.333333334 + x = 5.456901848

Solving for variable 'x'.

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

Add '4.333333334' to each side of the equation.
-4.333333334 + 4.333333334 + x = 5.456901848 + 4.333333334

Combine like terms: -4.333333334 + 4.333333334 = 0.000000000
0.000000000 + x = 5.456901848 + 4.333333334
x = 5.456901848 + 4.333333334

Combine like terms: 5.456901848 + 4.333333334 = 9.790235182
x = 9.790235182

Simplifying
x = 9.790235182


Subproblem 2
x + -4.333333334 = -5.456901848

Simplifying
x + -4.333333334 = -5.456901848

Reorder the terms:
-4.333333334 + x = -5.456901848

Solving
-4.333333334 + x = -5.456901848

Solving for variable 'x'.

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

Add '4.333333334' to each side of the equation.
-4.333333334 + 4.333333334 + x = -5.456901848 + 4.333333334

Combine like terms: -4.333333334 + 4.333333334 = 0.000000000
0.000000000 + x = -5.456901848 + 4.333333334
x = -5.456901848 + 4.333333334

Combine like terms: -5.456901848 + 4.333333334 = -1.123568514
x = -1.123568514

Simplifying
x = -1.123568514


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.790235182, -1.123568514}

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