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Simplifying p(p + -1) = 90 Reorder the terms: p(-1 + p) = 90 (-1 * p + p * p) = 90 (-1p + p2) = 90 Solving -1p + p2 = 90 Solving for variable 'p'. Reorder the terms: -90 + -1p + p2 = 90 + -90 Combine like terms: 90 + -90 = 0 -90 + -1p + p2 = 0 Factor a trinomial. (-9 + -1p)(10 + -1p) = 0Subproblem 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 '(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 = 10Solution
p = {-9, 10}
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