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Simplifying -1s5 = 2s3 + -8s Reorder the terms: -1s5 = -8s + 2s3 Solving -1s5 = -8s + 2s3 Solving for variable 's'. Reorder the terms: 8s + -2s3 + -1s5 = -8s + 2s3 + 8s + -2s3 Reorder the terms: 8s + -2s3 + -1s5 = -8s + 8s + 2s3 + -2s3 Combine like terms: -8s + 8s = 0 8s + -2s3 + -1s5 = 0 + 2s3 + -2s3 8s + -2s3 + -1s5 = 2s3 + -2s3 Combine like terms: 2s3 + -2s3 = 0 8s + -2s3 + -1s5 = 0 Factor out the Greatest Common Factor (GCF), 's'. s(8 + -2s2 + -1s4) = 0 Factor a trinomial. s((2 + -1s2)(4 + s2)) = 0Subproblem 1
Set the factor 's' equal to zero and attempt to solve: Simplifying s = 0 Solving s = 0 Move all terms containing s to the left, all other terms to the right. Simplifying s = 0Subproblem 2
Set the factor '(2 + -1s2)' equal to zero and attempt to solve: Simplifying 2 + -1s2 = 0 Solving 2 + -1s2 = 0 Move all terms containing s to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1s2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1s2 = 0 + -2 -1s2 = 0 + -2 Combine like terms: 0 + -2 = -2 -1s2 = -2 Divide each side by '-1'. s2 = 2 Simplifying s2 = 2 Take the square root of each side: s = {-1.414213562, 1.414213562}Subproblem 3
Set the factor '(4 + s2)' equal to zero and attempt to solve: Simplifying 4 + s2 = 0 Solving 4 + s2 = 0 Move all terms containing s to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + s2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + s2 = 0 + -4 s2 = 0 + -4 Combine like terms: 0 + -4 = -4 s2 = -4 Simplifying s2 = -4 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
s = {0, -1.414213562, 1.414213562}
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