3x^2-42x+17=0

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Solution for 3x^2-42x+17=0 equation: 


Simplifying
3x2 + -42x + 17 = 0

Reorder the terms:
17 + -42x + 3x2 = 0

Solving
17 + -42x + 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 + -14x + x2 = 0

Move the constant term to the right:

Add '-5.666666667' to each side of the equation.
5.666666667 + -14x + -5.666666667 + x2 = 0 + -5.666666667

Reorder the terms:
5.666666667 + -5.666666667 + -14x + x2 = 0 + -5.666666667

Combine like terms: 5.666666667 + -5.666666667 = 0.000000000
0.000000000 + -14x + x2 = 0 + -5.666666667
-14x + x2 = 0 + -5.666666667

Combine like terms: 0 + -5.666666667 = -5.666666667
-14x + x2 = -5.666666667

The x term is -14x.  Take half its coefficient (-7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
-14x + 49 + x2 = -5.666666667 + 49

Reorder the terms:
49 + -14x + x2 = -5.666666667 + 49

Combine like terms: -5.666666667 + 49 = 43.333333333
49 + -14x + x2 = 43.333333333

Factor a perfect square on the left side:
(x + -7)(x + -7) = 43.333333333

Calculate the square root of the right side: 6.582805886

Break this problem into two subproblems by setting 
(x + -7) equal to 6.582805886 and -6.582805886.


Subproblem 1
x + -7 = 6.582805886

Simplifying
x + -7 = 6.582805886

Reorder the terms:
-7 + x = 6.582805886

Solving
-7 + x = 6.582805886

Solving for variable 'x'.

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

Add '7' to each side of the equation.
-7 + 7 + x = 6.582805886 + 7

Combine like terms: -7 + 7 = 0
0 + x = 6.582805886 + 7
x = 6.582805886 + 7

Combine like terms: 6.582805886 + 7 = 13.582805886
x = 13.582805886

Simplifying
x = 13.582805886


Subproblem 2
x + -7 = -6.582805886

Simplifying
x + -7 = -6.582805886

Reorder the terms:
-7 + x = -6.582805886

Solving
-7 + x = -6.582805886

Solving for variable 'x'.

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

Add '7' to each side of the equation.
-7 + 7 + x = -6.582805886 + 7

Combine like terms: -7 + 7 = 0
0 + x = -6.582805886 + 7
x = -6.582805886 + 7

Combine like terms: -6.582805886 + 7 = 0.417194114
x = 0.417194114

Simplifying
x = 0.417194114


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {13.582805886, 0.417194114}

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