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Simplifying 4p2 + -32 = -28p Reorder the terms: -32 + 4p2 = -28p Solving -32 + 4p2 = -28p Solving for variable 'p'. Reorder the terms: -32 + 28p + 4p2 = -28p + 28p Combine like terms: -28p + 28p = 0 -32 + 28p + 4p2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-8 + 7p + p2) = 0 Factor a trinomial. 4((-8 + -1p)(1 + -1p)) = 0 Ignore the factor 4.Subproblem 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 '(1 + -1p)' equal to zero and attempt to solve: Simplifying 1 + -1p = 0 Solving 1 + -1p = 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 + -1p = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1p = 0 + -1 -1p = 0 + -1 Combine like terms: 0 + -1 = -1 -1p = -1 Divide each side by '-1'. p = 1 Simplifying p = 1Solution
p = {-8, 1}
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