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Simplifying 10p2d2 + 7pds = 12s2 Reorder the terms: 7dps + 10d2p2 = 12s2 Solving 7dps + 10d2p2 = 12s2 Solving for variable 'd'. Combine like terms: 12s2 + -12s2 = 0 7dps + 10d2p2 + -12s2 = 0 Factor a trinomial. (5dp + -4s)(2dp + 3s) = 0Subproblem 1
Set the factor '(5dp + -4s)' equal to zero and attempt to solve: Simplifying 5dp + -4s = 0 Solving 5dp + -4s = 0 Move all terms containing d to the left, all other terms to the right. Add '4s' to each side of the equation. 5dp + -4s + 4s = 0 + 4s Combine like terms: -4s + 4s = 0 5dp + 0 = 0 + 4s 5dp = 0 + 4s Remove the zero: 5dp = 4s Divide each side by '5p'. d = 0.8p-1s Simplifying d = 0.8p-1sSubproblem 2
Set the factor '(2dp + 3s)' equal to zero and attempt to solve: Simplifying 2dp + 3s = 0 Solving 2dp + 3s = 0 Move all terms containing d to the left, all other terms to the right. Add '-3s' to each side of the equation. 2dp + 3s + -3s = 0 + -3s Combine like terms: 3s + -3s = 0 2dp + 0 = 0 + -3s 2dp = 0 + -3s Remove the zero: 2dp = -3s Divide each side by '2p'. d = -1.5p-1s Simplifying d = -1.5p-1sSolution
d = {0.8p-1s, -1.5p-1s}
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