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Simplifying 30p2 = -15 + 55p Solving 30p2 = -15 + 55p Solving for variable 'p'. Reorder the terms: 15 + -55p + 30p2 = -15 + 55p + 15 + -55p Reorder the terms: 15 + -55p + 30p2 = -15 + 15 + 55p + -55p Combine like terms: -15 + 15 = 0 15 + -55p + 30p2 = 0 + 55p + -55p 15 + -55p + 30p2 = 55p + -55p Combine like terms: 55p + -55p = 0 15 + -55p + 30p2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(3 + -11p + 6p2) = 0 Factor a trinomial. 5((1 + -3p)(3 + -2p)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(1 + -3p)' equal to zero and attempt to solve: Simplifying 1 + -3p = 0 Solving 1 + -3p = 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 + -3p = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3p = 0 + -1 -3p = 0 + -1 Combine like terms: 0 + -1 = -1 -3p = -1 Divide each side by '-3'. p = 0.3333333333 Simplifying p = 0.3333333333Subproblem 2
Set the factor '(3 + -2p)' equal to zero and attempt to solve: Simplifying 3 + -2p = 0 Solving 3 + -2p = 0 Move all terms containing p to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -2p = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2p = 0 + -3 -2p = 0 + -3 Combine like terms: 0 + -3 = -3 -2p = -3 Divide each side by '-2'. p = 1.5 Simplifying p = 1.5Solution
p = {0.3333333333, 1.5}
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