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Simplifying 0 = p2 + -4p + -32 Reorder the terms: 0 = -32 + -4p + p2 Solving 0 = -32 + -4p + p2 Solving for variable 'p'. Combine like terms: 0 + 32 = 32 32 + 4p + -1p2 = -32 + -4p + p2 + 32 + 4p + -1p2 Reorder the terms: 32 + 4p + -1p2 = -32 + 32 + -4p + 4p + p2 + -1p2 Combine like terms: -32 + 32 = 0 32 + 4p + -1p2 = 0 + -4p + 4p + p2 + -1p2 32 + 4p + -1p2 = -4p + 4p + p2 + -1p2 Combine like terms: -4p + 4p = 0 32 + 4p + -1p2 = 0 + p2 + -1p2 32 + 4p + -1p2 = p2 + -1p2 Combine like terms: p2 + -1p2 = 0 32 + 4p + -1p2 = 0 Factor a trinomial. (8 + -1p)(4 + p) = 0Subproblem 1
Set the factor '(8 + -1p)' equal to zero and attempt to solve: Simplifying 8 + -1p = 0 Solving 8 + -1p = 0 Move all terms containing p to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1p = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1p = 0 + -8 -1p = 0 + -8 Combine like terms: 0 + -8 = -8 -1p = -8 Divide each side by '-1'. p = 8 Simplifying p = 8Subproblem 2
Set the factor '(4 + p)' equal to zero and attempt to solve: Simplifying 4 + p = 0 Solving 4 + p = 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 + p = 0 + -4 Combine like terms: 4 + -4 = 0 0 + p = 0 + -4 p = 0 + -4 Combine like terms: 0 + -4 = -4 p = -4 Simplifying p = -4Solution
p = {8, -4}
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