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Simplifying p2 + -35p + -92 = -6p2 + 6 Reorder the terms: -92 + -35p + p2 = -6p2 + 6 Reorder the terms: -92 + -35p + p2 = 6 + -6p2 Solving -92 + -35p + p2 = 6 + -6p2 Solving for variable 'p'. Reorder the terms: -92 + -6 + -35p + p2 + 6p2 = 6 + -6p2 + -6 + 6p2 Combine like terms: -92 + -6 = -98 -98 + -35p + p2 + 6p2 = 6 + -6p2 + -6 + 6p2 Combine like terms: p2 + 6p2 = 7p2 -98 + -35p + 7p2 = 6 + -6p2 + -6 + 6p2 Reorder the terms: -98 + -35p + 7p2 = 6 + -6 + -6p2 + 6p2 Combine like terms: 6 + -6 = 0 -98 + -35p + 7p2 = 0 + -6p2 + 6p2 -98 + -35p + 7p2 = -6p2 + 6p2 Combine like terms: -6p2 + 6p2 = 0 -98 + -35p + 7p2 = 0 Factor out the Greatest Common Factor (GCF), '7'. 7(-14 + -5p + p2) = 0 Factor a trinomial. 7((-2 + -1p)(7 + -1p)) = 0 Ignore the factor 7.Subproblem 1
Set the factor '(-2 + -1p)' equal to zero and attempt to solve: Simplifying -2 + -1p = 0 Solving -2 + -1p = 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 + -1p = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1p = 0 + 2 -1p = 0 + 2 Combine like terms: 0 + 2 = 2 -1p = 2 Divide each side by '-1'. p = -2 Simplifying p = -2Subproblem 2
Set the factor '(7 + -1p)' equal to zero and attempt to solve: Simplifying 7 + -1p = 0 Solving 7 + -1p = 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 + -1p = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1p = 0 + -7 -1p = 0 + -7 Combine like terms: 0 + -7 = -7 -1p = -7 Divide each side by '-1'. p = 7 Simplifying p = 7Solution
p = {-2, 7}
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