6x^2-17x+29=3x+8

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Solution for 6x^2-17x+29=3x+8 equation: 


Simplifying
6x2 + -17x + 29 = 3x + 8

Reorder the terms:
29 + -17x + 6x2 = 3x + 8

Reorder the terms:
29 + -17x + 6x2 = 8 + 3x

Solving
29 + -17x + 6x2 = 8 + 3x

Solving for variable 'x'.

Reorder the terms:
29 + -8 + -17x + -3x + 6x2 = 8 + 3x + -8 + -3x

Combine like terms: 29 + -8 = 21
21 + -17x + -3x + 6x2 = 8 + 3x + -8 + -3x

Combine like terms: -17x + -3x = -20x
21 + -20x + 6x2 = 8 + 3x + -8 + -3x

Reorder the terms:
21 + -20x + 6x2 = 8 + -8 + 3x + -3x

Combine like terms: 8 + -8 = 0
21 + -20x + 6x2 = 0 + 3x + -3x
21 + -20x + 6x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
21 + -20x + 6x2 = 0

Begin completing the square.  Divide all terms by
6 the coefficient of the squared term: 

Divide each side by '6'.
3.5 + -3.333333333x + x2 = 0

Move the constant term to the right:

Add '-3.5' to each side of the equation.
3.5 + -3.333333333x + -3.5 + x2 = 0 + -3.5

Reorder the terms:
3.5 + -3.5 + -3.333333333x + x2 = 0 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + -3.333333333x + x2 = 0 + -3.5
-3.333333333x + x2 = 0 + -3.5

Combine like terms: 0 + -3.5 = -3.5
-3.333333333x + x2 = -3.5

The x term is -3.333333333x.  Take half its coefficient (-1.666666667).
Square it (2.777777779) and add it to both sides.

Add '2.777777779' to each side of the equation.
-3.333333333x + 2.777777779 + x2 = -3.5 + 2.777777779

Reorder the terms:
2.777777779 + -3.333333333x + x2 = -3.5 + 2.777777779

Combine like terms: -3.5 + 2.777777779 = -0.722222221
2.777777779 + -3.333333333x + x2 = -0.722222221

Factor a perfect square on the left side:
(x + -1.666666667)(x + -1.666666667) = -0.722222221

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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