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Simplifying 3p2 + -5p = 4p2 + -35p + 56 Reorder the terms: -5p + 3p2 = 4p2 + -35p + 56 Reorder the terms: -5p + 3p2 = 56 + -35p + 4p2 Solving -5p + 3p2 = 56 + -35p + 4p2 Solving for variable 'p'. Reorder the terms: -56 + -5p + 35p + 3p2 + -4p2 = 56 + -35p + 4p2 + -56 + 35p + -4p2 Combine like terms: -5p + 35p = 30p -56 + 30p + 3p2 + -4p2 = 56 + -35p + 4p2 + -56 + 35p + -4p2 Combine like terms: 3p2 + -4p2 = -1p2 -56 + 30p + -1p2 = 56 + -35p + 4p2 + -56 + 35p + -4p2 Reorder the terms: -56 + 30p + -1p2 = 56 + -56 + -35p + 35p + 4p2 + -4p2 Combine like terms: 56 + -56 = 0 -56 + 30p + -1p2 = 0 + -35p + 35p + 4p2 + -4p2 -56 + 30p + -1p2 = -35p + 35p + 4p2 + -4p2 Combine like terms: -35p + 35p = 0 -56 + 30p + -1p2 = 0 + 4p2 + -4p2 -56 + 30p + -1p2 = 4p2 + -4p2 Combine like terms: 4p2 + -4p2 = 0 -56 + 30p + -1p2 = 0 Factor a trinomial. (-28 + p)(2 + -1p) = 0Subproblem 1
Set the factor '(-28 + p)' equal to zero and attempt to solve: Simplifying -28 + p = 0 Solving -28 + p = 0 Move all terms containing p to the left, all other terms to the right. Add '28' to each side of the equation. -28 + 28 + p = 0 + 28 Combine like terms: -28 + 28 = 0 0 + p = 0 + 28 p = 0 + 28 Combine like terms: 0 + 28 = 28 p = 28 Simplifying p = 28Subproblem 2
Set the factor '(2 + -1p)' equal to zero and attempt to solve: Simplifying 2 + -1p = 0 Solving 2 + -1p = 0 Move all terms containing p to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1p = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1p = 0 + -2 -1p = 0 + -2 Combine like terms: 0 + -2 = -2 -1p = -2 Divide each side by '-1'. p = 2 Simplifying p = 2Solution
p = {28, 2}
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