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Simplifying 104p2 + -161p + 28 = -1p2 Reorder the terms: 28 + -161p + 104p2 = -1p2 Solving 28 + -161p + 104p2 = -1p2 Solving for variable 'p'. Combine like terms: 104p2 + p2 = 105p2 28 + -161p + 105p2 = -1p2 + p2 Combine like terms: -1p2 + p2 = 0 28 + -161p + 105p2 = 0 Factor out the Greatest Common Factor (GCF), '7'. 7(4 + -23p + 15p2) = 0 Factor a trinomial. 7((1 + -5p)(4 + -3p)) = 0 Ignore the factor 7.Subproblem 1
Set the factor '(1 + -5p)' equal to zero and attempt to solve: Simplifying 1 + -5p = 0 Solving 1 + -5p = 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 + -5p = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -5p = 0 + -1 -5p = 0 + -1 Combine like terms: 0 + -1 = -1 -5p = -1 Divide each side by '-5'. p = 0.2 Simplifying p = 0.2Subproblem 2
Set the factor '(4 + -3p)' equal to zero and attempt to solve: Simplifying 4 + -3p = 0 Solving 4 + -3p = 0 Move all terms containing p to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -3p = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -3p = 0 + -4 -3p = 0 + -4 Combine like terms: 0 + -4 = -4 -3p = -4 Divide each side by '-3'. p = 1.333333333 Simplifying p = 1.333333333Solution
p = {0.2, 1.333333333}
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