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

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


Simplifying
0 = x4 + -9x2 + 14

Reorder the terms:
0 = 14 + -9x2 + x4

Solving
0 = 14 + -9x2 + x4

Solving for variable 'x'.

Combine like terms: 0 + -14 = -14
-14 + 9x2 + -1x4 = 14 + -9x2 + x4 + -14 + 9x2 + -1x4

Reorder the terms:
-14 + 9x2 + -1x4 = 14 + -14 + -9x2 + 9x2 + x4 + -1x4

Combine like terms: 14 + -14 = 0
-14 + 9x2 + -1x4 = 0 + -9x2 + 9x2 + x4 + -1x4
-14 + 9x2 + -1x4 = -9x2 + 9x2 + x4 + -1x4

Combine like terms: -9x2 + 9x2 = 0
-14 + 9x2 + -1x4 = 0 + x4 + -1x4
-14 + 9x2 + -1x4 = x4 + -1x4

Combine like terms: x4 + -1x4 = 0
-14 + 9x2 + -1x4 = 0

Factor a trinomial.
(-7 + x2)(2 + -1x2) = 0


Subproblem 1
Set the factor '(-7 + x2)' equal to zero and attempt to solve:

Simplifying
-7 + x2 = 0

Solving
-7 + x2 = 0

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

Add '7' to each side of the equation.
-7 + 7 + x2 = 0 + 7

Combine like terms: -7 + 7 = 0
0 + x2 = 0 + 7
x2 = 0 + 7

Combine like terms: 0 + 7 = 7
x2 = 7

Simplifying
x2 = 7

Take the square root of each side:
x = {-2.645751311, 2.645751311}

Subproblem 2
Set the factor '(2 + -1x2)' equal to zero and attempt to solve:

Simplifying
2 + -1x2 = 0

Solving
2 + -1x2 = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x2 = 0 + -2
-1x2 = 0 + -2

Combine like terms: 0 + -2 = -2
-1x2 = -2

Divide each side by '-1'.
x2 = 2

Simplifying
x2 = 2

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

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