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Simplifying 40s2 + -82sd + 40d2 = 0 Reorder the terms: -82ds + 40d2 + 40s2 = 0 Solving -82ds + 40d2 + 40s2 = 0 Solving for variable 'd'. Factor out the Greatest Common Factor (GCF), '2'. 2(-41ds + 20d2 + 20s2) = 0 Factor a trinomial. 2((4d + -5s)(5d + -4s)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(4d + -5s)' equal to zero and attempt to solve: Simplifying 4d + -5s = 0 Solving 4d + -5s = 0 Move all terms containing d to the left, all other terms to the right. Add '5s' to each side of the equation. 4d + -5s + 5s = 0 + 5s Combine like terms: -5s + 5s = 0 4d + 0 = 0 + 5s 4d = 0 + 5s Remove the zero: 4d = 5s Divide each side by '4'. d = 1.25s Simplifying d = 1.25sSubproblem 2
Set the factor '(5d + -4s)' equal to zero and attempt to solve: Simplifying 5d + -4s = 0 Solving 5d + -4s = 0 Move all terms containing d to the left, all other terms to the right. Add '4s' to each side of the equation. 5d + -4s + 4s = 0 + 4s Combine like terms: -4s + 4s = 0 5d + 0 = 0 + 4s 5d = 0 + 4s Remove the zero: 5d = 4s Divide each side by '5'. d = 0.8s Simplifying d = 0.8sSolution
d = {1.25s, 0.8s}
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