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Simplifying 8p2 = -128 + -80p Solving 8p2 = -128 + -80p Solving for variable 'p'. Reorder the terms: 128 + 80p + 8p2 = -128 + -80p + 128 + 80p Reorder the terms: 128 + 80p + 8p2 = -128 + 128 + -80p + 80p Combine like terms: -128 + 128 = 0 128 + 80p + 8p2 = 0 + -80p + 80p 128 + 80p + 8p2 = -80p + 80p Combine like terms: -80p + 80p = 0 128 + 80p + 8p2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(16 + 10p + p2) = 0 Factor a trinomial. 8((8 + p)(2 + p)) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(8 + p)' equal to zero and attempt to solve: Simplifying 8 + p = 0 Solving 8 + p = 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 + p = 0 + -8 Combine like terms: 8 + -8 = 0 0 + p = 0 + -8 p = 0 + -8 Combine like terms: 0 + -8 = -8 p = -8 Simplifying p = -8Subproblem 2
Set the factor '(2 + p)' equal to zero and attempt to solve: Simplifying 2 + p = 0 Solving 2 + p = 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 + p = 0 + -2 Combine like terms: 2 + -2 = 0 0 + p = 0 + -2 p = 0 + -2 Combine like terms: 0 + -2 = -2 p = -2 Simplifying p = -2Solution
p = {-8, -2}
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