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Simplifying 4p2 + 16p = 180 Reorder the terms: 16p + 4p2 = 180 Solving 16p + 4p2 = 180 Solving for variable 'p'. Reorder the terms: -180 + 16p + 4p2 = 180 + -180 Combine like terms: 180 + -180 = 0 -180 + 16p + 4p2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-45 + 4p + p2) = 0 Factor a trinomial. 4((-9 + -1p)(5 + -1p)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-9 + -1p)' equal to zero and attempt to solve: Simplifying -9 + -1p = 0 Solving -9 + -1p = 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 + -1p = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -1p = 0 + 9 -1p = 0 + 9 Combine like terms: 0 + 9 = 9 -1p = 9 Divide each side by '-1'. p = -9 Simplifying p = -9Subproblem 2
Set the factor '(5 + -1p)' equal to zero and attempt to solve: Simplifying 5 + -1p = 0 Solving 5 + -1p = 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 + -1p = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1p = 0 + -5 -1p = 0 + -5 Combine like terms: 0 + -5 = -5 -1p = -5 Divide each side by '-1'. p = 5 Simplifying p = 5Solution
p = {-9, 5}
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