3x^2-21x+17=0

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Solution for 3x^2-21x+17=0 equation: 


Simplifying
3x2 + -21x + 17 = 0

Reorder the terms:
17 + -21x + 3x2 = 0

Solving
17 + -21x + 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'.
5.666666667 + -7x + x2 = 0

Move the constant term to the right:

Add '-5.666666667' to each side of the equation.
5.666666667 + -7x + -5.666666667 + x2 = 0 + -5.666666667

Reorder the terms:
5.666666667 + -5.666666667 + -7x + x2 = 0 + -5.666666667

Combine like terms: 5.666666667 + -5.666666667 = 0.000000000
0.000000000 + -7x + x2 = 0 + -5.666666667
-7x + x2 = 0 + -5.666666667

Combine like terms: 0 + -5.666666667 = -5.666666667
-7x + x2 = -5.666666667

The x term is -7x.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7x + 12.25 + x2 = -5.666666667 + 12.25

Reorder the terms:
12.25 + -7x + x2 = -5.666666667 + 12.25

Combine like terms: -5.666666667 + 12.25 = 6.583333333
12.25 + -7x + x2 = 6.583333333

Factor a perfect square on the left side:
(x + -3.5)(x + -3.5) = 6.583333333

Calculate the square root of the right side: 2.56580072

Break this problem into two subproblems by setting 
(x + -3.5) equal to 2.56580072 and -2.56580072.


Subproblem 1
x + -3.5 = 2.56580072

Simplifying
x + -3.5 = 2.56580072

Reorder the terms:
-3.5 + x = 2.56580072

Solving
-3.5 + x = 2.56580072

Solving for variable 'x'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + x = 2.56580072 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + x = 2.56580072 + 3.5
x = 2.56580072 + 3.5

Combine like terms: 2.56580072 + 3.5 = 6.06580072
x = 6.06580072

Simplifying
x = 6.06580072


Subproblem 2
x + -3.5 = -2.56580072

Simplifying
x + -3.5 = -2.56580072

Reorder the terms:
-3.5 + x = -2.56580072

Solving
-3.5 + x = -2.56580072

Solving for variable 'x'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + x = -2.56580072 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + x = -2.56580072 + 3.5
x = -2.56580072 + 3.5

Combine like terms: -2.56580072 + 3.5 = 0.93419928
x = 0.93419928

Simplifying
x = 0.93419928


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.06580072, 0.93419928}

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