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Simplifying s2 + 3sd + -40d2 = 0 Reorder the terms: 3ds + -40d2 + s2 = 0 Solving 3ds + -40d2 + s2 = 0 Solving for variable 'd'. Factor a trinomial. (-8d + -1s)(5d + -1s) = 0Subproblem 1
Set the factor '(-8d + -1s)' equal to zero and attempt to solve: Simplifying -8d + -1s = 0 Solving -8d + -1s = 0 Move all terms containing d to the left, all other terms to the right. Add 's' to each side of the equation. -8d + -1s + s = 0 + s Combine like terms: -1s + s = 0 -8d + 0 = 0 + s -8d = 0 + s Remove the zero: -8d = s Divide each side by '-8'. d = -0.125s Simplifying d = -0.125sSubproblem 2
Set the factor '(5d + -1s)' equal to zero and attempt to solve: Simplifying 5d + -1s = 0 Solving 5d + -1s = 0 Move all terms containing d to the left, all other terms to the right. Add 's' to each side of the equation. 5d + -1s + s = 0 + s Combine like terms: -1s + s = 0 5d + 0 = 0 + s 5d = 0 + s Remove the zero: 5d = s Divide each side by '5'. d = 0.2s Simplifying d = 0.2sSolution
d = {-0.125s, 0.2s}
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