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Simplifying 64s4 + -96s2 + 36 = 0 Reorder the terms: 36 + -96s2 + 64s4 = 0 Solving 36 + -96s2 + 64s4 = 0 Solving for variable 's'. Factor out the Greatest Common Factor (GCF), '4'. 4(9 + -24s2 + 16s4) = 0 Factor a trinomial. 4((3 + -4s2)(3 + -4s2)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(3 + -4s2)' equal to zero and attempt to solve: Simplifying 3 + -4s2 = 0 Solving 3 + -4s2 = 0 Move all terms containing s to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -4s2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -4s2 = 0 + -3 -4s2 = 0 + -3 Combine like terms: 0 + -3 = -3 -4s2 = -3 Divide each side by '-4'. s2 = 0.75 Simplifying s2 = 0.75 Take the square root of each side: s = {-0.866025404, 0.866025404}Subproblem 2
Set the factor '(3 + -4s2)' equal to zero and attempt to solve: Simplifying 3 + -4s2 = 0 Solving 3 + -4s2 = 0 Move all terms containing s to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -4s2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -4s2 = 0 + -3 -4s2 = 0 + -3 Combine like terms: 0 + -3 = -3 -4s2 = -3 Divide each side by '-4'. s2 = 0.75 Simplifying s2 = 0.75 Take the square root of each side: s = {-0.866025404, 0.866025404}Solution
s = {-0.866025404, 0.866025404, -0.866025404, 0.866025404}
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