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Simplifying -17p + -11 + 2p2 = -2p2 + 9p + 3 Reorder the terms: -11 + -17p + 2p2 = -2p2 + 9p + 3 Reorder the terms: -11 + -17p + 2p2 = 3 + 9p + -2p2 Solving -11 + -17p + 2p2 = 3 + 9p + -2p2 Solving for variable 'p'. Reorder the terms: -11 + -3 + -17p + -9p + 2p2 + 2p2 = 3 + 9p + -2p2 + -3 + -9p + 2p2 Combine like terms: -11 + -3 = -14 -14 + -17p + -9p + 2p2 + 2p2 = 3 + 9p + -2p2 + -3 + -9p + 2p2 Combine like terms: -17p + -9p = -26p -14 + -26p + 2p2 + 2p2 = 3 + 9p + -2p2 + -3 + -9p + 2p2 Combine like terms: 2p2 + 2p2 = 4p2 -14 + -26p + 4p2 = 3 + 9p + -2p2 + -3 + -9p + 2p2 Reorder the terms: -14 + -26p + 4p2 = 3 + -3 + 9p + -9p + -2p2 + 2p2 Combine like terms: 3 + -3 = 0 -14 + -26p + 4p2 = 0 + 9p + -9p + -2p2 + 2p2 -14 + -26p + 4p2 = 9p + -9p + -2p2 + 2p2 Combine like terms: 9p + -9p = 0 -14 + -26p + 4p2 = 0 + -2p2 + 2p2 -14 + -26p + 4p2 = -2p2 + 2p2 Combine like terms: -2p2 + 2p2 = 0 -14 + -26p + 4p2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-7 + -13p + 2p2) = 0 Factor a trinomial. 2((-1 + -2p)(7 + -1p)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1 + -2p)' equal to zero and attempt to solve: Simplifying -1 + -2p = 0 Solving -1 + -2p = 0 Move all terms containing p to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -2p = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -2p = 0 + 1 -2p = 0 + 1 Combine like terms: 0 + 1 = 1 -2p = 1 Divide each side by '-2'. p = -0.5 Simplifying p = -0.5Subproblem 2
Set the factor '(7 + -1p)' equal to zero and attempt to solve: Simplifying 7 + -1p = 0 Solving 7 + -1p = 0 Move all terms containing p to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1p = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1p = 0 + -7 -1p = 0 + -7 Combine like terms: 0 + -7 = -7 -1p = -7 Divide each side by '-1'. p = 7 Simplifying p = 7Solution
p = {-0.5, 7}
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