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Simplifying 31s2 + -17s + 8 + 9s2 + -6s + -5 = 0 Reorder the terms: 8 + -5 + -17s + -6s + 31s2 + 9s2 = 0 Combine like terms: 8 + -5 = 3 3 + -17s + -6s + 31s2 + 9s2 = 0 Combine like terms: -17s + -6s = -23s 3 + -23s + 31s2 + 9s2 = 0 Combine like terms: 31s2 + 9s2 = 40s2 3 + -23s + 40s2 = 0 Solving 3 + -23s + 40s2 = 0 Solving for variable 's'. Factor a trinomial. (1 + -5s)(3 + -8s) = 0Subproblem 1
Set the factor '(1 + -5s)' equal to zero and attempt to solve: Simplifying 1 + -5s = 0 Solving 1 + -5s = 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 + -5s = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -5s = 0 + -1 -5s = 0 + -1 Combine like terms: 0 + -1 = -1 -5s = -1 Divide each side by '-5'. s = 0.2 Simplifying s = 0.2Subproblem 2
Set the factor '(3 + -8s)' equal to zero and attempt to solve: Simplifying 3 + -8s = 0 Solving 3 + -8s = 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 + -8s = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -8s = 0 + -3 -8s = 0 + -3 Combine like terms: 0 + -3 = -3 -8s = -3 Divide each side by '-8'. s = 0.375 Simplifying s = 0.375Solution
s = {0.2, 0.375}
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