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Simplifying 7p2 + 5 = 3p2 + 9p Reorder the terms: 5 + 7p2 = 3p2 + 9p Reorder the terms: 5 + 7p2 = 9p + 3p2 Solving 5 + 7p2 = 9p + 3p2 Solving for variable 'p'. Reorder the terms: 5 + -9p + 7p2 + -3p2 = 9p + 3p2 + -9p + -3p2 Combine like terms: 7p2 + -3p2 = 4p2 5 + -9p + 4p2 = 9p + 3p2 + -9p + -3p2 Reorder the terms: 5 + -9p + 4p2 = 9p + -9p + 3p2 + -3p2 Combine like terms: 9p + -9p = 0 5 + -9p + 4p2 = 0 + 3p2 + -3p2 5 + -9p + 4p2 = 3p2 + -3p2 Combine like terms: 3p2 + -3p2 = 0 5 + -9p + 4p2 = 0 Factor a trinomial. (1 + -1p)(5 + -4p) = 0Subproblem 1
Set the factor '(1 + -1p)' equal to zero and attempt to solve: Simplifying 1 + -1p = 0 Solving 1 + -1p = 0 Move all terms containing p to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1p = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1p = 0 + -1 -1p = 0 + -1 Combine like terms: 0 + -1 = -1 -1p = -1 Divide each side by '-1'. p = 1 Simplifying p = 1Subproblem 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 = {1, 1.25}
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