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Simplifying 38p2 + 28 = -82p + 8p2 Reorder the terms: 28 + 38p2 = -82p + 8p2 Solving 28 + 38p2 = -82p + 8p2 Solving for variable 'p'. Reorder the terms: 28 + 82p + 38p2 + -8p2 = -82p + 8p2 + 82p + -8p2 Combine like terms: 38p2 + -8p2 = 30p2 28 + 82p + 30p2 = -82p + 8p2 + 82p + -8p2 Reorder the terms: 28 + 82p + 30p2 = -82p + 82p + 8p2 + -8p2 Combine like terms: -82p + 82p = 0 28 + 82p + 30p2 = 0 + 8p2 + -8p2 28 + 82p + 30p2 = 8p2 + -8p2 Combine like terms: 8p2 + -8p2 = 0 28 + 82p + 30p2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(14 + 41p + 15p2) = 0 Factor a trinomial. 2((7 + 3p)(2 + 5p)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(7 + 3p)' equal to zero and attempt to solve: Simplifying 7 + 3p = 0 Solving 7 + 3p = 0 Move all terms containing p to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + 3p = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 3p = 0 + -7 3p = 0 + -7 Combine like terms: 0 + -7 = -7 3p = -7 Divide each side by '3'. p = -2.333333333 Simplifying p = -2.333333333Subproblem 2
Set the factor '(2 + 5p)' equal to zero and attempt to solve: Simplifying 2 + 5p = 0 Solving 2 + 5p = 0 Move all terms containing p to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + 5p = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 5p = 0 + -2 5p = 0 + -2 Combine like terms: 0 + -2 = -2 5p = -2 Divide each side by '5'. p = -0.4 Simplifying p = -0.4Solution
p = {-2.333333333, -0.4}
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