4y^2+6y+14=0

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Solution for 4y^2+6y+14=0 equation: 


Simplifying
4y2 + 6y + 14 = 0

Reorder the terms:
14 + 6y + 4y2 = 0

Solving
14 + 6y + 4y2 = 0

Solving for variable 'y'.

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

Ignore the factor 2.

Subproblem 1
Set the factor '(7 + 3y + 2y2)' equal to zero and attempt to solve:

Simplifying
7 + 3y + 2y2 = 0

Solving
7 + 3y + 2y2 = 0

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

Divide each side by '2'.
3.5 + 1.5y + y2 = 0

Move the constant term to the right:

Add '-3.5' to each side of the equation.
3.5 + 1.5y + -3.5 + y2 = 0 + -3.5

Reorder the terms:
3.5 + -3.5 + 1.5y + y2 = 0 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + 1.5y + y2 = 0 + -3.5
1.5y + y2 = 0 + -3.5

Combine like terms: 0 + -3.5 = -3.5
1.5y + y2 = -3.5

The y term is 1.5y.  Take half its coefficient (0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
1.5y + 0.5625 + y2 = -3.5 + 0.5625

Reorder the terms:
0.5625 + 1.5y + y2 = -3.5 + 0.5625

Combine like terms: -3.5 + 0.5625 = -2.9375
0.5625 + 1.5y + y2 = -2.9375

Factor a perfect square on the left side:
(y + 0.75)(y + 0.75) = -2.9375

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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