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Simplifying 3s2 + 10s + -7 + 11s2 + -8s + 12 + s + -7 = 0 Reorder the terms: -7 + 12 + -7 + 10s + -8s + s + 3s2 + 11s2 = 0 Combine like terms: -7 + 12 = 5 5 + -7 + 10s + -8s + s + 3s2 + 11s2 = 0 Combine like terms: 5 + -7 = -2 -2 + 10s + -8s + s + 3s2 + 11s2 = 0 Combine like terms: 10s + -8s = 2s -2 + 2s + s + 3s2 + 11s2 = 0 Combine like terms: 2s + s = 3s -2 + 3s + 3s2 + 11s2 = 0 Combine like terms: 3s2 + 11s2 = 14s2 -2 + 3s + 14s2 = 0 Solving -2 + 3s + 14s2 = 0 Solving for variable 's'. Factor a trinomial. (-1 + -2s)(2 + -7s) = 0Subproblem 1
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 = -0.5Subproblem 2
Set the factor '(2 + -7s)' equal to zero and attempt to solve: Simplifying 2 + -7s = 0 Solving 2 + -7s = 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 + -7s = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -7s = 0 + -2 -7s = 0 + -2 Combine like terms: 0 + -2 = -2 -7s = -2 Divide each side by '-7'. s = 0.2857142857 Simplifying s = 0.2857142857Solution
s = {-0.5, 0.2857142857}
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