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Simplifying t2 + 3tp + -40p2 = 0 Reorder the terms: 3pt + -40p2 + t2 = 0 Solving 3pt + -40p2 + t2 = 0 Solving for variable 'p'. Factor a trinomial. (-8p + -1t)(5p + -1t) = 0Subproblem 1
Set the factor '(-8p + -1t)' equal to zero and attempt to solve: Simplifying -8p + -1t = 0 Solving -8p + -1t = 0 Move all terms containing p to the left, all other terms to the right. Add 't' to each side of the equation. -8p + -1t + t = 0 + t Combine like terms: -1t + t = 0 -8p + 0 = 0 + t -8p = 0 + t Remove the zero: -8p = t Divide each side by '-8'. p = -0.125t Simplifying p = -0.125tSubproblem 2
Set the factor '(5p + -1t)' equal to zero and attempt to solve: Simplifying 5p + -1t = 0 Solving 5p + -1t = 0 Move all terms containing p to the left, all other terms to the right. Add 't' to each side of the equation. 5p + -1t + t = 0 + t Combine like terms: -1t + t = 0 5p + 0 = 0 + t 5p = 0 + t Remove the zero: 5p = t Divide each side by '5'. p = 0.2t Simplifying p = 0.2tSolution
p = {-0.125t, 0.2t}
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