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Simplifying 6p2 = -40 + 31p Solving 6p2 = -40 + 31p Solving for variable 'p'. Reorder the terms: 40 + -31p + 6p2 = -40 + 31p + 40 + -31p Reorder the terms: 40 + -31p + 6p2 = -40 + 40 + 31p + -31p Combine like terms: -40 + 40 = 0 40 + -31p + 6p2 = 0 + 31p + -31p 40 + -31p + 6p2 = 31p + -31p Combine like terms: 31p + -31p = 0 40 + -31p + 6p2 = 0 Factor a trinomial. (5 + -2p)(8 + -3p) = 0Subproblem 1
Set the factor '(5 + -2p)' equal to zero and attempt to solve: Simplifying 5 + -2p = 0 Solving 5 + -2p = 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 + -2p = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2p = 0 + -5 -2p = 0 + -5 Combine like terms: 0 + -5 = -5 -2p = -5 Divide each side by '-2'. p = 2.5 Simplifying p = 2.5Subproblem 2
Set the factor '(8 + -3p)' equal to zero and attempt to solve: Simplifying 8 + -3p = 0 Solving 8 + -3p = 0 Move all terms containing p to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -3p = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -3p = 0 + -8 -3p = 0 + -8 Combine like terms: 0 + -8 = -8 -3p = -8 Divide each side by '-3'. p = 2.666666667 Simplifying p = 2.666666667Solution
p = {2.5, 2.666666667}
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