16x^4=81a^4

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Solution for 16x^4=81a^4 equation:


Simplifying
16x4 = 81a4

Solving
16x4 = 81a4

Solving for variable 'x'.

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

Divide each side by '16'.
x4 = 5.0625a4

Simplifying
x4 = 5.0625a4

Reorder the terms:
-5.0625a4 + x4 = 5.0625a4 + -5.0625a4

Combine like terms: 5.0625a4 + -5.0625a4 = 0.0000
-5.0625a4 + x4 = 0.0000

Factor a difference between two squares.
(2.25a2 + x2)(-2.25a2 + x2) = 0.0000

Factor a difference between two squares.
(2.25a2 + x2)((1.5a + x)(-1.5a + x)) = 0.0000

Subproblem 1

Set the factor '(2.25a2 + x2)' equal to zero and attempt to solve: Simplifying 2.25a2 + x2 = 0 Solving 2.25a2 + x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '-2.25a2' to each side of the equation. 2.25a2 + -2.25a2 + x2 = 0 + -2.25a2 Combine like terms: 2.25a2 + -2.25a2 = 0.00 0.00 + x2 = 0 + -2.25a2 x2 = 0 + -2.25a2 Remove the zero: x2 = -2.25a2 Simplifying x2 = -2.25a2 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 '(1.5a + x)' equal to zero and attempt to solve: Simplifying 1.5a + x = 0 Solving 1.5a + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1.5a' to each side of the equation. 1.5a + -1.5a + x = 0 + -1.5a Combine like terms: 1.5a + -1.5a = 0.0 0.0 + x = 0 + -1.5a x = 0 + -1.5a Remove the zero: x = -1.5a Simplifying x = -1.5a

Subproblem 3

Set the factor '(-1.5a + x)' equal to zero and attempt to solve: Simplifying -1.5a + x = 0 Solving -1.5a + x = 0 Move all terms containing x to the left, all other terms to the right. Add '1.5a' to each side of the equation. -1.5a + 1.5a + x = 0 + 1.5a Combine like terms: -1.5a + 1.5a = 0.0 0.0 + x = 0 + 1.5a x = 0 + 1.5a Remove the zero: x = 1.5a Simplifying x = 1.5a

Solution

x = {-1.5a, 1.5a}

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