3x^2-20x+22=0

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Solution for 3x^2-20x+22=0 equation: 


Simplifying
3x2 + -20x + 22 = 0

Reorder the terms:
22 + -20x + 3x2 = 0

Solving
22 + -20x + 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'.
7.333333333 + -6.666666667x + x2 = 0

Move the constant term to the right:

Add '-7.333333333' to each side of the equation.
7.333333333 + -6.666666667x + -7.333333333 + x2 = 0 + -7.333333333

Reorder the terms:
7.333333333 + -7.333333333 + -6.666666667x + x2 = 0 + -7.333333333

Combine like terms: 7.333333333 + -7.333333333 = 0.000000000
0.000000000 + -6.666666667x + x2 = 0 + -7.333333333
-6.666666667x + x2 = 0 + -7.333333333

Combine like terms: 0 + -7.333333333 = -7.333333333
-6.666666667x + x2 = -7.333333333

The x term is -6.666666667x.  Take half its coefficient (-3.333333334).
Square it (11.11111112) and add it to both sides.

Add '11.11111112' to each side of the equation.
-6.666666667x + 11.11111112 + x2 = -7.333333333 + 11.11111112

Reorder the terms:
11.11111112 + -6.666666667x + x2 = -7.333333333 + 11.11111112

Combine like terms: -7.333333333 + 11.11111112 = 3.777777787
11.11111112 + -6.666666667x + x2 = 3.777777787

Factor a perfect square on the left side:
(x + -3.333333334)(x + -3.333333334) = 3.777777787

Calculate the square root of the right side: 1.943650634

Break this problem into two subproblems by setting 
(x + -3.333333334) equal to 1.943650634 and -1.943650634.


Subproblem 1
x + -3.333333334 = 1.943650634

Simplifying
x + -3.333333334 = 1.943650634

Reorder the terms:
-3.333333334 + x = 1.943650634

Solving
-3.333333334 + x = 1.943650634

Solving for variable 'x'.

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

Add '3.333333334' to each side of the equation.
-3.333333334 + 3.333333334 + x = 1.943650634 + 3.333333334

Combine like terms: -3.333333334 + 3.333333334 = 0.000000000
0.000000000 + x = 1.943650634 + 3.333333334
x = 1.943650634 + 3.333333334

Combine like terms: 1.943650634 + 3.333333334 = 5.276983968
x = 5.276983968

Simplifying
x = 5.276983968


Subproblem 2
x + -3.333333334 = -1.943650634

Simplifying
x + -3.333333334 = -1.943650634

Reorder the terms:
-3.333333334 + x = -1.943650634

Solving
-3.333333334 + x = -1.943650634

Solving for variable 'x'.

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

Add '3.333333334' to each side of the equation.
-3.333333334 + 3.333333334 + x = -1.943650634 + 3.333333334

Combine like terms: -3.333333334 + 3.333333334 = 0.000000000
0.000000000 + x = -1.943650634 + 3.333333334
x = -1.943650634 + 3.333333334

Combine like terms: -1.943650634 + 3.333333334 = 1.3896827
x = 1.3896827

Simplifying
x = 1.3896827


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.276983968, 1.3896827}

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