2y^2-3y+5+y^2-6y+9=0

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Solution for 2y^2-3y+5+y^2-6y+9=0 equation: 


Simplifying
2y2 + -3y + 5 + y2 + -6y + 9 = 0

Reorder the terms:
5 + 9 + -3y + -6y + 2y2 + y2 = 0

Combine like terms: 5 + 9 = 14
14 + -3y + -6y + 2y2 + y2 = 0

Combine like terms: -3y + -6y = -9y
14 + -9y + 2y2 + y2 = 0

Combine like terms: 2y2 + y2 = 3y2
14 + -9y + 3y2 = 0

Solving
14 + -9y + 3y2 = 0

Solving for variable 'y'.

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

Divide each side by '3'.
4.666666667 + -3y + y2 = 0

Move the constant term to the right:

Add '-4.666666667' to each side of the equation.
4.666666667 + -3y + -4.666666667 + y2 = 0 + -4.666666667

Reorder the terms:
4.666666667 + -4.666666667 + -3y + y2 = 0 + -4.666666667

Combine like terms: 4.666666667 + -4.666666667 = 0.000000000
0.000000000 + -3y + y2 = 0 + -4.666666667
-3y + y2 = 0 + -4.666666667

Combine like terms: 0 + -4.666666667 = -4.666666667
-3y + y2 = -4.666666667

The y term is -3y.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3y + 2.25 + y2 = -4.666666667 + 2.25

Reorder the terms:
2.25 + -3y + y2 = -4.666666667 + 2.25

Combine like terms: -4.666666667 + 2.25 = -2.416666667
2.25 + -3y + y2 = -2.416666667

Factor a perfect square on the left side:
(y + -1.5)(y + -1.5) = -2.416666667

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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