x^2+x^4=272

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Solution for x^2+x^4=272 equation:


Simplifying
x2 + x4 = 272

Solving
x2 + x4 = 272

Solving for variable 'x'.

Reorder the terms:
-272 + x2 + x4 = 272 + -272

Combine like terms: 272 + -272 = 0
-272 + x2 + x4 = 0

Factor a trinomial.
(-17 + -1x2)(16 + -1x2) = 0

Factor a difference between two squares.
(-17 + -1x2)((4 + x)(4 + -1x)) = 0

Subproblem 1

Set the factor '(-17 + -1x2)' equal to zero and attempt to solve: Simplifying -17 + -1x2 = 0 Solving -17 + -1x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '17' to each side of the equation. -17 + 17 + -1x2 = 0 + 17 Combine like terms: -17 + 17 = 0 0 + -1x2 = 0 + 17 -1x2 = 0 + 17 Combine like terms: 0 + 17 = 17 -1x2 = 17 Divide each side by '-1'. x2 = -17 Simplifying x2 = -17 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.

Subproblem 2

Set the factor '(4 + x)' equal to zero and attempt to solve: Simplifying 4 + x = 0 Solving 4 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + x = 0 + -4 x = 0 + -4 Combine like terms: 0 + -4 = -4 x = -4 Simplifying x = -4

Subproblem 3

Set the factor '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4

Solution

x = {-4, 4}

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