3x^2-33x-7.7=0

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Solution for 3x^2-33x-7.7=0 equation: 


Simplifying
3x2 + -33x + -7.7 = 0

Reorder the terms:
-7.7 + -33x + 3x2 = 0

Solving
-7.7 + -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'.
-2.566666667 + -11x + x2 = 0

Move the constant term to the right:

Add '2.566666667' to each side of the equation.
-2.566666667 + -11x + 2.566666667 + x2 = 0 + 2.566666667

Reorder the terms:
-2.566666667 + 2.566666667 + -11x + x2 = 0 + 2.566666667

Combine like terms: -2.566666667 + 2.566666667 = 0.000000000
0.000000000 + -11x + x2 = 0 + 2.566666667
-11x + x2 = 0 + 2.566666667

Combine like terms: 0 + 2.566666667 = 2.566666667
-11x + x2 = 2.566666667

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 = 2.566666667 + 30.25

Reorder the terms:
30.25 + -11x + x2 = 2.566666667 + 30.25

Combine like terms: 2.566666667 + 30.25 = 32.816666667
30.25 + -11x + x2 = 32.816666667

Factor a perfect square on the left side:
(x + -5.5)(x + -5.5) = 32.816666667

Calculate the square root of the right side: 5.728583304

Break this problem into two subproblems by setting 
(x + -5.5) equal to 5.728583304 and -5.728583304.


Subproblem 1
x + -5.5 = 5.728583304

Simplifying
x + -5.5 = 5.728583304

Reorder the terms:
-5.5 + x = 5.728583304

Solving
-5.5 + x = 5.728583304

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 = 5.728583304 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + x = 5.728583304 + 5.5
x = 5.728583304 + 5.5

Combine like terms: 5.728583304 + 5.5 = 11.228583304
x = 11.228583304

Simplifying
x = 11.228583304


Subproblem 2
x + -5.5 = -5.728583304

Simplifying
x + -5.5 = -5.728583304

Reorder the terms:
-5.5 + x = -5.728583304

Solving
-5.5 + x = -5.728583304

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 = -5.728583304 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + x = -5.728583304 + 5.5
x = -5.728583304 + 5.5

Combine like terms: -5.728583304 + 5.5 = -0.228583304
x = -0.228583304

Simplifying
x = -0.228583304


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {11.228583304, -0.228583304}

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