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Simplifying 400 = -1p2 + -3p + 488 Reorder the terms: 400 = 488 + -3p + -1p2 Solving 400 = 488 + -3p + -1p2 Solving for variable 'p'. Combine like terms: 400 + -488 = -88 -88 + 3p + p2 = 488 + -3p + -1p2 + -488 + 3p + p2 Reorder the terms: -88 + 3p + p2 = 488 + -488 + -3p + 3p + -1p2 + p2 Combine like terms: 488 + -488 = 0 -88 + 3p + p2 = 0 + -3p + 3p + -1p2 + p2 -88 + 3p + p2 = -3p + 3p + -1p2 + p2 Combine like terms: -3p + 3p = 0 -88 + 3p + p2 = 0 + -1p2 + p2 -88 + 3p + p2 = -1p2 + p2 Combine like terms: -1p2 + p2 = 0 -88 + 3p + p2 = 0 Factor a trinomial. (-11 + -1p)(8 + -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 '(8 + -1p)' equal to zero and attempt to solve: Simplifying 8 + -1p = 0 Solving 8 + -1p = 0 Move all terms containing p to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1p = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1p = 0 + -8 -1p = 0 + -8 Combine like terms: 0 + -8 = -8 -1p = -8 Divide each side by '-1'. p = 8 Simplifying p = 8Solution
p = {-11, 8}
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