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Simplifying -3p2 + 10p + 5 = -8p2 Reorder the terms: 5 + 10p + -3p2 = -8p2 Solving 5 + 10p + -3p2 = -8p2 Solving for variable 'p'. Combine like terms: -3p2 + 8p2 = 5p2 5 + 10p + 5p2 = -8p2 + 8p2 Combine like terms: -8p2 + 8p2 = 0 5 + 10p + 5p2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(1 + 2p + p2) = 0 Factor a trinomial. 5((1 + p)(1 + p)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(1 + p)' equal to zero and attempt to solve: Simplifying 1 + p = 0 Solving 1 + p = 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 + p = 0 + -1 Combine like terms: 1 + -1 = 0 0 + p = 0 + -1 p = 0 + -1 Combine like terms: 0 + -1 = -1 p = -1 Simplifying p = -1Subproblem 2
Set the factor '(1 + p)' equal to zero and attempt to solve: Simplifying 1 + p = 0 Solving 1 + p = 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 + p = 0 + -1 Combine like terms: 1 + -1 = 0 0 + p = 0 + -1 p = 0 + -1 Combine like terms: 0 + -1 = -1 p = -1 Simplifying p = -1Solution
p = {-1, -1}
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