32s^4=8s^2

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Solution for 32s^4=8s^2 equation:


Simplifying
32s4 = 8s2

Solving
32s4 = 8s2

Solving for variable 's'.

Reorder the terms:
-8s2 + 32s4 = 8s2 + -8s2

Combine like terms: 8s2 + -8s2 = 0
-8s2 + 32s4 = 0

Factor out the Greatest Common Factor (GCF), '8s2'.
8s2(-1 + 4s2) = 0

Factor a difference between two squares.
8s2((1 + 2s)(-1 + 2s)) = 0

Ignore the factor 8.

Subproblem 1

Set the factor 's2' equal to zero and attempt to solve: Simplifying s2 = 0 Solving s2 = 0 Move all terms containing s to the left, all other terms to the right. Simplifying s2 = 0 Take the square root of each side: s = {0}

Subproblem 2

Set the factor '(1 + 2s)' equal to zero and attempt to solve: Simplifying 1 + 2s = 0 Solving 1 + 2s = 0 Move all terms containing s to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 2s = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2s = 0 + -1 2s = 0 + -1 Combine like terms: 0 + -1 = -1 2s = -1 Divide each side by '2'. s = -0.5 Simplifying s = -0.5

Subproblem 3

Set the factor '(-1 + 2s)' equal to zero and attempt to solve: Simplifying -1 + 2s = 0 Solving -1 + 2s = 0 Move all terms containing s to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + 2s = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 2s = 0 + 1 2s = 0 + 1 Combine like terms: 0 + 1 = 1 2s = 1 Divide each side by '2'. s = 0.5 Simplifying s = 0.5

Solution

s = {0, -0.5, 0.5}

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