8y^2-4y+14=0

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Solution for 8y^2-4y+14=0 equation:


Simplifying
8y2 + -4y + 14 = 0

Reorder the terms:
14 + -4y + 8y2 = 0

Solving
14 + -4y + 8y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '2'.
2(7 + -2y + 4y2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(7 + -2y + 4y2)' equal to zero and attempt to solve:

Simplifying
7 + -2y + 4y2 = 0

Solving
7 + -2y + 4y2 = 0

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

Divide each side by '4'.
1.75 + -0.5y + y2 = 0

Move the constant term to the right:

Add '-1.75' to each side of the equation.
1.75 + -0.5y + -1.75 + y2 = 0 + -1.75

Reorder the terms:
1.75 + -1.75 + -0.5y + y2 = 0 + -1.75

Combine like terms: 1.75 + -1.75 = 0.00
0.00 + -0.5y + y2 = 0 + -1.75
-0.5y + y2 = 0 + -1.75

Combine like terms: 0 + -1.75 = -1.75
-0.5y + y2 = -1.75

The y term is -0.5y.  Take half its coefficient (-0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
-0.5y + 0.0625 + y2 = -1.75 + 0.0625

Reorder the terms:
0.0625 + -0.5y + y2 = -1.75 + 0.0625

Combine like terms: -1.75 + 0.0625 = -1.6875
0.0625 + -0.5y + y2 = -1.6875

Factor a perfect square on the left side:
(y + -0.25)(y + -0.25) = -1.6875

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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