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Simplifying 200 = -1p2 + -4p + 317 Reorder the terms: 200 = 317 + -4p + -1p2 Solving 200 = 317 + -4p + -1p2 Solving for variable 'p'. Combine like terms: 200 + -317 = -117 -117 + 4p + p2 = 317 + -4p + -1p2 + -317 + 4p + p2 Reorder the terms: -117 + 4p + p2 = 317 + -317 + -4p + 4p + -1p2 + p2 Combine like terms: 317 + -317 = 0 -117 + 4p + p2 = 0 + -4p + 4p + -1p2 + p2 -117 + 4p + p2 = -4p + 4p + -1p2 + p2 Combine like terms: -4p + 4p = 0 -117 + 4p + p2 = 0 + -1p2 + p2 -117 + 4p + p2 = -1p2 + p2 Combine like terms: -1p2 + p2 = 0 -117 + 4p + p2 = 0 Factor a trinomial. (-13 + -1p)(9 + -1p) = 0Subproblem 1
Set the factor '(-13 + -1p)' equal to zero and attempt to solve: Simplifying -13 + -1p = 0 Solving -13 + -1p = 0 Move all terms containing p to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + -1p = 0 + 13 Combine like terms: -13 + 13 = 0 0 + -1p = 0 + 13 -1p = 0 + 13 Combine like terms: 0 + 13 = 13 -1p = 13 Divide each side by '-1'. p = -13 Simplifying p = -13Subproblem 2
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 = 9Solution
p = {-13, 9}
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