16a^4-1=0

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Solution for 16a^4-1=0 equation:


Simplifying
16a4 + -1 = 0

Reorder the terms:
-1 + 16a4 = 0

Solving
-1 + 16a4 = 0

Solving for variable 'a'.

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

Add '1' to each side of the equation.
-1 + 1 + 16a4 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 16a4 = 0 + 1
16a4 = 0 + 1

Combine like terms: 0 + 1 = 1
16a4 = 1

Divide each side by '16'.
a4 = 0.0625

Simplifying
a4 = 0.0625

Reorder the terms:
-0.0625 + a4 = 0.0625 + -0.0625

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

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

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

Subproblem 1

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

Subproblem 3

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

Solution

a = {-0.5, 0.5}

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