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Simplifying 7p = p2 + 10 Reorder the terms: 7p = 10 + p2 Solving 7p = 10 + p2 Solving for variable 'p'. Reorder the terms: -10 + 7p + -1p2 = 10 + p2 + -10 + -1p2 Reorder the terms: -10 + 7p + -1p2 = 10 + -10 + p2 + -1p2 Combine like terms: 10 + -10 = 0 -10 + 7p + -1p2 = 0 + p2 + -1p2 -10 + 7p + -1p2 = p2 + -1p2 Combine like terms: p2 + -1p2 = 0 -10 + 7p + -1p2 = 0 Factor a trinomial. (-5 + p)(2 + -1p) = 0Subproblem 1
Set the factor '(-5 + p)' equal to zero and attempt to solve: Simplifying -5 + p = 0 Solving -5 + p = 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 + p = 0 + 5 Combine like terms: -5 + 5 = 0 0 + p = 0 + 5 p = 0 + 5 Combine like terms: 0 + 5 = 5 p = 5 Simplifying p = 5Subproblem 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 = {5, 2}
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