14v^2+8v+32=0

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Solution for 14v^2+8v+32=0 equation: 


Simplifying
14v2 + 8v + 32 = 0

Reorder the terms:
32 + 8v + 14v2 = 0

Solving
32 + 8v + 14v2 = 0

Solving for variable 'v'.

Factor out the Greatest Common Factor (GCF), '2'.
2(16 + 4v + 7v2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(16 + 4v + 7v2)' equal to zero and attempt to solve:

Simplifying
16 + 4v + 7v2 = 0

Solving
16 + 4v + 7v2 = 0

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

Divide each side by '7'.
2.285714286 + 0.5714285714v + v2 = 0

Move the constant term to the right:

Add '-2.285714286' to each side of the equation.
2.285714286 + 0.5714285714v + -2.285714286 + v2 = 0 + -2.285714286

Reorder the terms:
2.285714286 + -2.285714286 + 0.5714285714v + v2 = 0 + -2.285714286

Combine like terms: 2.285714286 + -2.285714286 = 0.000000000
0.000000000 + 0.5714285714v + v2 = 0 + -2.285714286
0.5714285714v + v2 = 0 + -2.285714286

Combine like terms: 0 + -2.285714286 = -2.285714286
0.5714285714v + v2 = -2.285714286

The v term is 0.5714285714v.  Take half its coefficient (0.2857142857).
Square it (0.08163265305) and add it to both sides.

Add '0.08163265305' to each side of the equation.
0.5714285714v + 0.08163265305 + v2 = -2.285714286 + 0.08163265305

Reorder the terms:
0.08163265305 + 0.5714285714v + v2 = -2.285714286 + 0.08163265305

Combine like terms: -2.285714286 + 0.08163265305 = -2.20408163295
0.08163265305 + 0.5714285714v + v2 = -2.20408163295

Factor a perfect square on the left side:
(v + 0.2857142857)(v + 0.2857142857) = -2.20408163295

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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