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Simplifying 8s2 = 30 + 34s Solving 8s2 = 30 + 34s Solving for variable 's'. Reorder the terms: -30 + -34s + 8s2 = 30 + 34s + -30 + -34s Reorder the terms: -30 + -34s + 8s2 = 30 + -30 + 34s + -34s Combine like terms: 30 + -30 = 0 -30 + -34s + 8s2 = 0 + 34s + -34s -30 + -34s + 8s2 = 34s + -34s Combine like terms: 34s + -34s = 0 -30 + -34s + 8s2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-15 + -17s + 4s2) = 0 Factor a trinomial. 2((-3 + -4s)(5 + -1s)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-3 + -4s)' equal to zero and attempt to solve: Simplifying -3 + -4s = 0 Solving -3 + -4s = 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 + -4s = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -4s = 0 + 3 -4s = 0 + 3 Combine like terms: 0 + 3 = 3 -4s = 3 Divide each side by '-4'. s = -0.75 Simplifying s = -0.75Subproblem 2
Set the factor '(5 + -1s)' equal to zero and attempt to solve: Simplifying 5 + -1s = 0 Solving 5 + -1s = 0 Move all terms containing s to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1s = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1s = 0 + -5 -1s = 0 + -5 Combine like terms: 0 + -5 = -5 -1s = -5 Divide each side by '-1'. s = 5 Simplifying s = 5Solution
s = {-0.75, 5}
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