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Simplifying 15p2 + -81p + 84 = 0 Reorder the terms: 84 + -81p + 15p2 = 0 Solving 84 + -81p + 15p2 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), '3'. 3(28 + -27p + 5p2) = 0 Factor a trinomial. 3((7 + -5p)(4 + -1p)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(7 + -5p)' equal to zero and attempt to solve: Simplifying 7 + -5p = 0 Solving 7 + -5p = 0 Move all terms containing p to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -5p = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -5p = 0 + -7 -5p = 0 + -7 Combine like terms: 0 + -7 = -7 -5p = -7 Divide each side by '-5'. p = 1.4 Simplifying p = 1.4Subproblem 2
Set the factor '(4 + -1p)' equal to zero and attempt to solve: Simplifying 4 + -1p = 0 Solving 4 + -1p = 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 + -1p = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1p = 0 + -4 -1p = 0 + -4 Combine like terms: 0 + -4 = -4 -1p = -4 Divide each side by '-1'. p = 4 Simplifying p = 4Solution
p = {1.4, 4}
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