3x^2+22x+33=0

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Solution for 3x^2+22x+33=0 equation: 


Simplifying
3x2 + 22x + 33 = 0

Reorder the terms:
33 + 22x + 3x2 = 0

Solving
33 + 22x + 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 + 7.333333333x + x2 = 0

Move the constant term to the right:

Add '-11' to each side of the equation.
11 + 7.333333333x + -11 + x2 = 0 + -11

Reorder the terms:
11 + -11 + 7.333333333x + x2 = 0 + -11

Combine like terms: 11 + -11 = 0
0 + 7.333333333x + x2 = 0 + -11
7.333333333x + x2 = 0 + -11

Combine like terms: 0 + -11 = -11
7.333333333x + x2 = -11

The x term is 7.333333333x.  Take half its coefficient (3.666666667).
Square it (13.44444445) and add it to both sides.

Add '13.44444445' to each side of the equation.
7.333333333x + 13.44444445 + x2 = -11 + 13.44444445

Reorder the terms:
13.44444445 + 7.333333333x + x2 = -11 + 13.44444445

Combine like terms: -11 + 13.44444445 = 2.44444445
13.44444445 + 7.333333333x + x2 = 2.44444445

Factor a perfect square on the left side:
(x + 3.666666667)(x + 3.666666667) = 2.44444445

Calculate the square root of the right side: 1.563471922

Break this problem into two subproblems by setting 
(x + 3.666666667) equal to 1.563471922 and -1.563471922.


Subproblem 1
x + 3.666666667 = 1.563471922

Simplifying
x + 3.666666667 = 1.563471922

Reorder the terms:
3.666666667 + x = 1.563471922

Solving
3.666666667 + x = 1.563471922

Solving for variable 'x'.

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

Add '-3.666666667' to each side of the equation.
3.666666667 + -3.666666667 + x = 1.563471922 + -3.666666667

Combine like terms: 3.666666667 + -3.666666667 = 0.000000000
0.000000000 + x = 1.563471922 + -3.666666667
x = 1.563471922 + -3.666666667

Combine like terms: 1.563471922 + -3.666666667 = -2.103194745
x = -2.103194745

Simplifying
x = -2.103194745


Subproblem 2
x + 3.666666667 = -1.563471922

Simplifying
x + 3.666666667 = -1.563471922

Reorder the terms:
3.666666667 + x = -1.563471922

Solving
3.666666667 + x = -1.563471922

Solving for variable 'x'.

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

Add '-3.666666667' to each side of the equation.
3.666666667 + -3.666666667 + x = -1.563471922 + -3.666666667

Combine like terms: 3.666666667 + -3.666666667 = 0.000000000
0.000000000 + x = -1.563471922 + -3.666666667
x = -1.563471922 + -3.666666667

Combine like terms: -1.563471922 + -3.666666667 = -5.230138589
x = -5.230138589

Simplifying
x = -5.230138589


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-2.103194745, -5.230138589}

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