c^4-9c^2+14=0

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Solution for c^4-9c^2+14=0 equation: 


Simplifying
c4 + -9c2 + 14 = 0

Reorder the terms:
14 + -9c2 + c4 = 0

Solving
14 + -9c2 + c4 = 0

Solving for variable 'c'.

Factor a trinomial.
(2 + -1c2)(7 + -1c2) = 0


Subproblem 1
Set the factor '(2 + -1c2)' equal to zero and attempt to solve:

Simplifying
2 + -1c2 = 0

Solving
2 + -1c2 = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1c2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1c2 = 0 + -2
-1c2 = 0 + -2

Combine like terms: 0 + -2 = -2
-1c2 = -2

Divide each side by '-1'.
c2 = 2

Simplifying
c2 = 2

Take the square root of each side:
c = {-1.414213562, 1.414213562}

Subproblem 2
Set the factor '(7 + -1c2)' equal to zero and attempt to solve:

Simplifying
7 + -1c2 = 0

Solving
7 + -1c2 = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1c2 = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1c2 = 0 + -7
-1c2 = 0 + -7

Combine like terms: 0 + -7 = -7
-1c2 = -7

Divide each side by '-1'.
c2 = 7

Simplifying
c2 = 7

Take the square root of each side:
c = {-2.645751311, 2.645751311}
Solution
c = {-1.414213562, 1.414213562, -2.645751311, 2.645751311}

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