64a^4-4b^4=0

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Solution for 64a^4-4b^4=0 equation:


Simplifying
64a4 + -4b4 = 0

Solving
64a4 + -4b4 = 0

Solving for variable 'a'.

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

Add '4b4' to each side of the equation.
64a4 + -4b4 + 4b4 = 0 + 4b4

Combine like terms: -4b4 + 4b4 = 0
64a4 + 0 = 0 + 4b4
64a4 = 0 + 4b4
Remove the zero:
64a4 = 4b4

Divide each side by '64'.
a4 = 0.0625b4

Simplifying
a4 = 0.0625b4

Combine like terms: 0.0625b4 + -0.0625b4 = 0.0000
a4 + -0.0625b4 = 0.0000

Factor a difference between two squares.
(a2 + 0.25b2)(a2 + -0.25b2) = 0.0000

Factor a difference between two squares.
(a2 + 0.25b2)((a + 0.5b)(a + -0.5b)) = 0.0000

Subproblem 1

Set the factor '(a2 + 0.25b2)' equal to zero and attempt to solve: Simplifying a2 + 0.25b2 = 0 Solving a2 + 0.25b2 = 0 Move all terms containing a to the left, all other terms to the right. Add '-0.25b2' to each side of the equation. a2 + 0.25b2 + -0.25b2 = 0 + -0.25b2 Combine like terms: 0.25b2 + -0.25b2 = 0.00 a2 + 0.00 = 0 + -0.25b2 a2 = 0 + -0.25b2 Remove the zero: a2 = -0.25b2 Simplifying a2 = -0.25b2 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 '(a + 0.5b)' equal to zero and attempt to solve: Simplifying a + 0.5b = 0 Solving a + 0.5b = 0 Move all terms containing a to the left, all other terms to the right. Add '-0.5b' to each side of the equation. a + 0.5b + -0.5b = 0 + -0.5b Combine like terms: 0.5b + -0.5b = 0.0 a + 0.0 = 0 + -0.5b a = 0 + -0.5b Remove the zero: a = -0.5b Simplifying a = -0.5b

Subproblem 3

Set the factor '(a + -0.5b)' equal to zero and attempt to solve: Simplifying a + -0.5b = 0 Solving a + -0.5b = 0 Move all terms containing a to the left, all other terms to the right. Add '0.5b' to each side of the equation. a + -0.5b + 0.5b = 0 + 0.5b Combine like terms: -0.5b + 0.5b = 0.0 a + 0.0 = 0 + 0.5b a = 0 + 0.5b Remove the zero: a = 0.5b Simplifying a = 0.5b

Solution

a = {-0.5b, 0.5b}

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