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Simplifying 5p2 + -10p + -32 = 8 Reorder the terms: -32 + -10p + 5p2 = 8 Solving -32 + -10p + 5p2 = 8 Solving for variable 'p'. Reorder the terms: -32 + -8 + -10p + 5p2 = 8 + -8 Combine like terms: -32 + -8 = -40 -40 + -10p + 5p2 = 8 + -8 Combine like terms: 8 + -8 = 0 -40 + -10p + 5p2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-8 + -2p + p2) = 0 Factor a trinomial. 5((-2 + -1p)(4 + -1p)) = 0 Ignore the factor 5.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 '(4 + -1p)' equal to zero and attempt to solve: Simplifying 4 + -1p = 0 Solving 4 + -1p = 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 + -1p = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1p = 0 + -4 -1p = 0 + -4 Combine like terms: 0 + -4 = -4 -1p = -4 Divide each side by '-1'. p = 4 Simplifying p = 4Solution
p = {-2, 4}
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