21y^2-7y+14=

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Solution for 21y^2-7y+14= equation: 


Simplifying
21y2 + -7y + 14 = 0

Reorder the terms:
14 + -7y + 21y2 = 0

Solving
14 + -7y + 21y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '7'.
7(2 + -1y + 3y2) = 0

Ignore the factor 7.

Subproblem 1
Set the factor '(2 + -1y + 3y2)' equal to zero and attempt to solve:

Simplifying
2 + -1y + 3y2 = 0

Solving
2 + -1y + 3y2 = 0

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

Divide each side by '3'.
0.6666666667 + -0.3333333333y + y2 = 0

Move the constant term to the right:

Add '-0.6666666667' to each side of the equation.
0.6666666667 + -0.3333333333y + -0.6666666667 + y2 = 0 + -0.6666666667

Reorder the terms:
0.6666666667 + -0.6666666667 + -0.3333333333y + y2 = 0 + -0.6666666667

Combine like terms: 0.6666666667 + -0.6666666667 = 0.0000000000
0.0000000000 + -0.3333333333y + y2 = 0 + -0.6666666667
-0.3333333333y + y2 = 0 + -0.6666666667

Combine like terms: 0 + -0.6666666667 = -0.6666666667
-0.3333333333y + y2 = -0.6666666667

The y term is -0.3333333333y.  Take half its coefficient (-0.1666666667).
Square it (0.02777777779) and add it to both sides.

Add '0.02777777779' to each side of the equation.
-0.3333333333y + 0.02777777779 + y2 = -0.6666666667 + 0.02777777779

Reorder the terms:
0.02777777779 + -0.3333333333y + y2 = -0.6666666667 + 0.02777777779

Combine like terms: -0.6666666667 + 0.02777777779 = -0.63888888891
0.02777777779 + -0.3333333333y + y2 = -0.63888888891

Factor a perfect square on the left side:
(y + -0.1666666667)(y + -0.1666666667) = -0.63888888891

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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