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Simplifying 32p2 + 284p + -360 = 0 Reorder the terms: -360 + 284p + 32p2 = 0 Solving -360 + 284p + 32p2 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), '4'. 4(-90 + 71p + 8p2) = 0 Factor a trinomial. 4((-10 + -1p)(9 + -8p)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-10 + -1p)' equal to zero and attempt to solve: Simplifying -10 + -1p = 0 Solving -10 + -1p = 0 Move all terms containing p to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + -1p = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -1p = 0 + 10 -1p = 0 + 10 Combine like terms: 0 + 10 = 10 -1p = 10 Divide each side by '-1'. p = -10 Simplifying p = -10Subproblem 2
Set the factor '(9 + -8p)' equal to zero and attempt to solve: Simplifying 9 + -8p = 0 Solving 9 + -8p = 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 + -8p = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -8p = 0 + -9 -8p = 0 + -9 Combine like terms: 0 + -9 = -9 -8p = -9 Divide each side by '-8'. p = 1.125 Simplifying p = 1.125Solution
p = {-10, 1.125}
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