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Simplifying -5(7p + -5) + 3p(p + 5) = 0 Reorder the terms: -5(-5 + 7p) + 3p(p + 5) = 0 (-5 * -5 + 7p * -5) + 3p(p + 5) = 0 (25 + -35p) + 3p(p + 5) = 0 Reorder the terms: 25 + -35p + 3p(5 + p) = 0 25 + -35p + (5 * 3p + p * 3p) = 0 25 + -35p + (15p + 3p2) = 0 Combine like terms: -35p + 15p = -20p 25 + -20p + 3p2 = 0 Solving 25 + -20p + 3p2 = 0 Solving for variable 'p'. Factor a trinomial. (5 + -3p)(5 + -1p) = 0Subproblem 1
Set the factor '(5 + -3p)' equal to zero and attempt to solve: Simplifying 5 + -3p = 0 Solving 5 + -3p = 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 + -3p = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -3p = 0 + -5 -3p = 0 + -5 Combine like terms: 0 + -5 = -5 -3p = -5 Divide each side by '-3'. p = 1.666666667 Simplifying p = 1.666666667Subproblem 2
Set the factor '(5 + -1p)' equal to zero and attempt to solve: Simplifying 5 + -1p = 0 Solving 5 + -1p = 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 + -1p = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1p = 0 + -5 -1p = 0 + -5 Combine like terms: 0 + -5 = -5 -1p = -5 Divide each side by '-1'. p = 5 Simplifying p = 5Solution
p = {1.666666667, 5}
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