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Simplifying 85p = 4p2 + 100 Reorder the terms: 85p = 100 + 4p2 Solving 85p = 100 + 4p2 Solving for variable 'p'. Reorder the terms: -100 + 85p + -4p2 = 100 + 4p2 + -100 + -4p2 Reorder the terms: -100 + 85p + -4p2 = 100 + -100 + 4p2 + -4p2 Combine like terms: 100 + -100 = 0 -100 + 85p + -4p2 = 0 + 4p2 + -4p2 -100 + 85p + -4p2 = 4p2 + -4p2 Combine like terms: 4p2 + -4p2 = 0 -100 + 85p + -4p2 = 0 Factor a trinomial. (-20 + p)(5 + -4p) = 0Subproblem 1
Set the factor '(-20 + p)' equal to zero and attempt to solve: Simplifying -20 + p = 0 Solving -20 + p = 0 Move all terms containing p to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + p = 0 + 20 Combine like terms: -20 + 20 = 0 0 + p = 0 + 20 p = 0 + 20 Combine like terms: 0 + 20 = 20 p = 20 Simplifying p = 20Subproblem 2
Set the factor '(5 + -4p)' equal to zero and attempt to solve: Simplifying 5 + -4p = 0 Solving 5 + -4p = 0 Move all terms containing p to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -4p = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -4p = 0 + -5 -4p = 0 + -5 Combine like terms: 0 + -5 = -5 -4p = -5 Divide each side by '-4'. p = 1.25 Simplifying p = 1.25Solution
p = {20, 1.25}
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