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Simplifying 8(2p2 + 25p + -517) = 0 Reorder the terms: 8(-517 + 25p + 2p2) = 0 (-517 * 8 + 25p * 8 + 2p2 * 8) = 0 (-4136 + 200p + 16p2) = 0 Solving -4136 + 200p + 16p2 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), '8'. 8(-517 + 25p + 2p2) = 0 Factor a trinomial. 8((-47 + -2p)(11 + -1p)) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(-47 + -2p)' equal to zero and attempt to solve: Simplifying -47 + -2p = 0 Solving -47 + -2p = 0 Move all terms containing p to the left, all other terms to the right. Add '47' to each side of the equation. -47 + 47 + -2p = 0 + 47 Combine like terms: -47 + 47 = 0 0 + -2p = 0 + 47 -2p = 0 + 47 Combine like terms: 0 + 47 = 47 -2p = 47 Divide each side by '-2'. p = -23.5 Simplifying p = -23.5Subproblem 2
Set the factor '(11 + -1p)' equal to zero and attempt to solve: Simplifying 11 + -1p = 0 Solving 11 + -1p = 0 Move all terms containing p to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + -1p = 0 + -11 Combine like terms: 11 + -11 = 0 0 + -1p = 0 + -11 -1p = 0 + -11 Combine like terms: 0 + -11 = -11 -1p = -11 Divide each side by '-1'. p = 11 Simplifying p = 11Solution
p = {-23.5, 11}
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