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Simplifying 32p2 + -8p + -180 = 0 Reorder the terms: -180 + -8p + 32p2 = 0 Solving -180 + -8p + 32p2 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), '4'. 4(-45 + -2p + 8p2) = 0 Factor a trinomial. 4((-9 + -4p)(5 + -2p)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-9 + -4p)' equal to zero and attempt to solve: Simplifying -9 + -4p = 0 Solving -9 + -4p = 0 Move all terms containing p to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + -4p = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -4p = 0 + 9 -4p = 0 + 9 Combine like terms: 0 + 9 = 9 -4p = 9 Divide each side by '-4'. p = -2.25 Simplifying p = -2.25Subproblem 2
Set the factor '(5 + -2p)' equal to zero and attempt to solve: Simplifying 5 + -2p = 0 Solving 5 + -2p = 0 Move all terms containing p to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -2p = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2p = 0 + -5 -2p = 0 + -5 Combine like terms: 0 + -5 = -5 -2p = -5 Divide each side by '-2'. p = 2.5 Simplifying p = 2.5Solution
p = {-2.25, 2.5}
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