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Simplifying 5s(9s + -5)(5s + -1) = 0 Reorder the terms: 5s(-5 + 9s)(5s + -1) = 0 Reorder the terms: 5s(-5 + 9s)(-1 + 5s) = 0 Multiply (-5 + 9s) * (-1 + 5s) 5s(-5(-1 + 5s) + 9s * (-1 + 5s)) = 0 5s((-1 * -5 + 5s * -5) + 9s * (-1 + 5s)) = 0 5s((5 + -25s) + 9s * (-1 + 5s)) = 0 5s(5 + -25s + (-1 * 9s + 5s * 9s)) = 0 5s(5 + -25s + (-9s + 45s2)) = 0 Combine like terms: -25s + -9s = -34s 5s(5 + -34s + 45s2) = 0 (5 * 5s + -34s * 5s + 45s2 * 5s) = 0 (25s + -170s2 + 225s3) = 0 Solving 25s + -170s2 + 225s3 = 0 Solving for variable 's'. Factor out the Greatest Common Factor (GCF), '5s'. 5s(5 + -34s + 45s2) = 0 Factor a trinomial. 5s((1 + -5s)(5 + -9s)) = 0 Ignore the factor 5.Subproblem 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 '(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 3
Set the factor '(5 + -9s)' equal to zero and attempt to solve: Simplifying 5 + -9s = 0 Solving 5 + -9s = 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 + -9s = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -9s = 0 + -5 -9s = 0 + -5 Combine like terms: 0 + -5 = -5 -9s = -5 Divide each side by '-9'. s = 0.5555555556 Simplifying s = 0.5555555556Solution
s = {0, 0.2, 0.5555555556}
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