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Simplifying 200 = -1p2 + -6p + 255 Reorder the terms: 200 = 255 + -6p + -1p2 Solving 200 = 255 + -6p + -1p2 Solving for variable 'p'. Combine like terms: 200 + -255 = -55 -55 + 6p + p2 = 255 + -6p + -1p2 + -255 + 6p + p2 Reorder the terms: -55 + 6p + p2 = 255 + -255 + -6p + 6p + -1p2 + p2 Combine like terms: 255 + -255 = 0 -55 + 6p + p2 = 0 + -6p + 6p + -1p2 + p2 -55 + 6p + p2 = -6p + 6p + -1p2 + p2 Combine like terms: -6p + 6p = 0 -55 + 6p + p2 = 0 + -1p2 + p2 -55 + 6p + p2 = -1p2 + p2 Combine like terms: -1p2 + p2 = 0 -55 + 6p + p2 = 0 Factor a trinomial. (-11 + -1p)(5 + -1p) = 0Subproblem 1
Set the factor '(-11 + -1p)' equal to zero and attempt to solve: Simplifying -11 + -1p = 0 Solving -11 + -1p = 0 Move all terms containing p to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + -1p = 0 + 11 Combine like terms: -11 + 11 = 0 0 + -1p = 0 + 11 -1p = 0 + 11 Combine like terms: 0 + 11 = 11 -1p = 11 Divide each side by '-1'. p = -11 Simplifying p = -11Subproblem 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 = {-11, 5}
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