3x^2-33x-40=0

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Solution for 3x^2-33x-40=0 equation: 


Simplifying
3x2 + -33x + -40 = 0

Reorder the terms:
-40 + -33x + 3x2 = 0

Solving
-40 + -33x + 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'.
-13.33333333 + -11x + x2 = 0

Move the constant term to the right:

Add '13.33333333' to each side of the equation.
-13.33333333 + -11x + 13.33333333 + x2 = 0 + 13.33333333

Reorder the terms:
-13.33333333 + 13.33333333 + -11x + x2 = 0 + 13.33333333

Combine like terms: -13.33333333 + 13.33333333 = 0.00000000
0.00000000 + -11x + x2 = 0 + 13.33333333
-11x + x2 = 0 + 13.33333333

Combine like terms: 0 + 13.33333333 = 13.33333333
-11x + x2 = 13.33333333

The x term is -11x.  Take half its coefficient (-5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
-11x + 30.25 + x2 = 13.33333333 + 30.25

Reorder the terms:
30.25 + -11x + x2 = 13.33333333 + 30.25

Combine like terms: 13.33333333 + 30.25 = 43.58333333
30.25 + -11x + x2 = 43.58333333

Factor a perfect square on the left side:
(x + -5.5)(x + -5.5) = 43.58333333

Calculate the square root of the right side: 6.60176744

Break this problem into two subproblems by setting 
(x + -5.5) equal to 6.60176744 and -6.60176744.


Subproblem 1
x + -5.5 = 6.60176744

Simplifying
x + -5.5 = 6.60176744

Reorder the terms:
-5.5 + x = 6.60176744

Solving
-5.5 + x = 6.60176744

Solving for variable 'x'.

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

Add '5.5' to each side of the equation.
-5.5 + 5.5 + x = 6.60176744 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + x = 6.60176744 + 5.5
x = 6.60176744 + 5.5

Combine like terms: 6.60176744 + 5.5 = 12.10176744
x = 12.10176744

Simplifying
x = 12.10176744


Subproblem 2
x + -5.5 = -6.60176744

Simplifying
x + -5.5 = -6.60176744

Reorder the terms:
-5.5 + x = -6.60176744

Solving
-5.5 + x = -6.60176744

Solving for variable 'x'.

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

Add '5.5' to each side of the equation.
-5.5 + 5.5 + x = -6.60176744 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + x = -6.60176744 + 5.5
x = -6.60176744 + 5.5

Combine like terms: -6.60176744 + 5.5 = -1.10176744
x = -1.10176744

Simplifying
x = -1.10176744


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {12.10176744, -1.10176744}

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