x^4+14=9x^2

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


Simplifying
x4 + 14 = 9x2

Reorder the terms:
14 + x4 = 9x2

Solving
14 + x4 = 9x2

Solving for variable 'x'.

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

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

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

Subproblem 1

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}

Subproblem 2

Set the factor '(7 + -1x2)' equal to zero and attempt to solve: Simplifying 7 + -1x2 = 0 Solving 7 + -1x2 = 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 + -1x2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1x2 = 0 + -7 -1x2 = 0 + -7 Combine like terms: 0 + -7 = -7 -1x2 = -7 Divide each side by '-1'. x2 = 7 Simplifying x2 = 7 Take the square root of each side: x = {-2.645751311, 2.645751311}

Solution

x = {-1.414213562, 1.414213562, -2.645751311, 2.645751311}

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