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Simplifying 7p2 + -42p = -56 Reorder the terms: -42p + 7p2 = -56 Solving -42p + 7p2 = -56 Solving for variable 'p'. Reorder the terms: 56 + -42p + 7p2 = -56 + 56 Combine like terms: -56 + 56 = 0 56 + -42p + 7p2 = 0 Factor out the Greatest Common Factor (GCF), '7'. 7(8 + -6p + p2) = 0 Factor a trinomial. 7((2 + -1p)(4 + -1p)) = 0 Ignore the factor 7.Subproblem 1
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 = 2Subproblem 2
Set the factor '(4 + -1p)' equal to zero and attempt to solve: Simplifying 4 + -1p = 0 Solving 4 + -1p = 0 Move all terms containing p to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1p = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1p = 0 + -4 -1p = 0 + -4 Combine like terms: 0 + -4 = -4 -1p = -4 Divide each side by '-1'. p = 4 Simplifying p = 4Solution
p = {2, 4}
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