14v^4-23v^2+8=

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Solution for 14v^4-23v^2+8= equation: 


Simplifying
14v4 + -23v2 + 8 = 0

Reorder the terms:
8 + -23v2 + 14v4 = 0

Solving
8 + -23v2 + 14v4 = 0

Solving for variable 'v'.

Factor a trinomial.
(1 + -2v2)(8 + -7v2) = 0


Subproblem 1
Set the factor '(1 + -2v2)' equal to zero and attempt to solve:

Simplifying
1 + -2v2 = 0

Solving
1 + -2v2 = 0

Move all terms containing v to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + -2v2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2v2 = 0 + -1
-2v2 = 0 + -1

Combine like terms: 0 + -1 = -1
-2v2 = -1

Divide each side by '-2'.
v2 = 0.5

Simplifying
v2 = 0.5

Take the square root of each side:
v = {-0.707106781, 0.707106781}

Subproblem 2
Set the factor '(8 + -7v2)' equal to zero and attempt to solve:

Simplifying
8 + -7v2 = 0

Solving
8 + -7v2 = 0

Move all terms containing v to the left, all other terms to the right.

Add '-8' to each side of the equation.
8 + -8 + -7v2 = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -7v2 = 0 + -8
-7v2 = 0 + -8

Combine like terms: 0 + -8 = -8
-7v2 = -8

Divide each side by '-7'.
v2 = 1.142857143

Simplifying
v2 = 1.142857143

Take the square root of each side:
v = {-1.069044968, 1.069044968}
Solution
v = {-0.707106781, 0.707106781, -1.069044968, 1.069044968}

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