8x^2=x^4+16

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Solution for 8x^2=x^4+16 equation:


Simplifying
8x2 = x4 + 16

Reorder the terms:
8x2 = 16 + x4

Solving
8x2 = 16 + x4

Solving for variable 'x'.

Reorder the terms:
-16 + 8x2 + -1x4 = 16 + x4 + -16 + -1x4

Reorder the terms:
-16 + 8x2 + -1x4 = 16 + -16 + x4 + -1x4

Combine like terms: 16 + -16 = 0
-16 + 8x2 + -1x4 = 0 + x4 + -1x4
-16 + 8x2 + -1x4 = x4 + -1x4

Combine like terms: x4 + -1x4 = 0
-16 + 8x2 + -1x4 = 0

Factor a trinomial.
(-4 + x2)(4 + -1x2) = 0

Factor a difference between two squares.
((2 + x)(-2 + x))(4 + -1x2) = 0

Factor a difference between two squares.
((2 + x)(2 + -1x))(2 + x)(-2 + x) = 0

Subproblem 1

Set the factor '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 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 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Simplifying x = -2

Subproblem 2

Set the factor '(-2 + x)' equal to zero and attempt to solve: Simplifying -2 + x = 0 Solving -2 + x = 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 + x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + x = 0 + 2 x = 0 + 2 Combine like terms: 0 + 2 = 2 x = 2 Simplifying x = 2

Subproblem 3

Set the factor '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 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 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Simplifying x = -2

Subproblem 4

Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 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 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2

Solution

x = {-2, 2, -2, 2}

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