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Simplifying (s + -8)(s + 4) + (s + -8)(s + -5) = 0 Reorder the terms: (-8 + s)(s + 4) + (s + -8)(s + -5) = 0 Reorder the terms: (-8 + s)(4 + s) + (s + -8)(s + -5) = 0 Multiply (-8 + s) * (4 + s) (-8(4 + s) + s(4 + s)) + (s + -8)(s + -5) = 0 ((4 * -8 + s * -8) + s(4 + s)) + (s + -8)(s + -5) = 0 ((-32 + -8s) + s(4 + s)) + (s + -8)(s + -5) = 0 (-32 + -8s + (4 * s + s * s)) + (s + -8)(s + -5) = 0 (-32 + -8s + (4s + s2)) + (s + -8)(s + -5) = 0 Combine like terms: -8s + 4s = -4s (-32 + -4s + s2) + (s + -8)(s + -5) = 0 Reorder the terms: -32 + -4s + s2 + (-8 + s)(s + -5) = 0 Reorder the terms: -32 + -4s + s2 + (-8 + s)(-5 + s) = 0 Multiply (-8 + s) * (-5 + s) -32 + -4s + s2 + (-8(-5 + s) + s(-5 + s)) = 0 -32 + -4s + s2 + ((-5 * -8 + s * -8) + s(-5 + s)) = 0 -32 + -4s + s2 + ((40 + -8s) + s(-5 + s)) = 0 -32 + -4s + s2 + (40 + -8s + (-5 * s + s * s)) = 0 -32 + -4s + s2 + (40 + -8s + (-5s + s2)) = 0 Combine like terms: -8s + -5s = -13s -32 + -4s + s2 + (40 + -13s + s2) = 0 Reorder the terms: -32 + 40 + -4s + -13s + s2 + s2 = 0 Combine like terms: -32 + 40 = 8 8 + -4s + -13s + s2 + s2 = 0 Combine like terms: -4s + -13s = -17s 8 + -17s + s2 + s2 = 0 Combine like terms: s2 + s2 = 2s2 8 + -17s + 2s2 = 0 Solving 8 + -17s + 2s2 = 0 Solving for variable 's'. Factor a trinomial. (1 + -2s)(8 + -1s) = 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 '(8 + -1s)' equal to zero and attempt to solve: Simplifying 8 + -1s = 0 Solving 8 + -1s = 0 Move all terms containing s to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1s = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1s = 0 + -8 -1s = 0 + -8 Combine like terms: 0 + -8 = -8 -1s = -8 Divide each side by '-1'. s = 8 Simplifying s = 8Solution
s = {0.5, 8}
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