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Simplifying (2p + -1)(2p + -1) + -9(2p + -1) + 18 = 0 Reorder the terms: (-1 + 2p)(2p + -1) + -9(2p + -1) + 18 = 0 Reorder the terms: (-1 + 2p)(-1 + 2p) + -9(2p + -1) + 18 = 0 Multiply (-1 + 2p) * (-1 + 2p) (-1(-1 + 2p) + 2p * (-1 + 2p)) + -9(2p + -1) + 18 = 0 ((-1 * -1 + 2p * -1) + 2p * (-1 + 2p)) + -9(2p + -1) + 18 = 0 ((1 + -2p) + 2p * (-1 + 2p)) + -9(2p + -1) + 18 = 0 (1 + -2p + (-1 * 2p + 2p * 2p)) + -9(2p + -1) + 18 = 0 (1 + -2p + (-2p + 4p2)) + -9(2p + -1) + 18 = 0 Combine like terms: -2p + -2p = -4p (1 + -4p + 4p2) + -9(2p + -1) + 18 = 0 Reorder the terms: 1 + -4p + 4p2 + -9(-1 + 2p) + 18 = 0 1 + -4p + 4p2 + (-1 * -9 + 2p * -9) + 18 = 0 1 + -4p + 4p2 + (9 + -18p) + 18 = 0 Reorder the terms: 1 + 9 + 18 + -4p + -18p + 4p2 = 0 Combine like terms: 1 + 9 = 10 10 + 18 + -4p + -18p + 4p2 = 0 Combine like terms: 10 + 18 = 28 28 + -4p + -18p + 4p2 = 0 Combine like terms: -4p + -18p = -22p 28 + -22p + 4p2 = 0 Solving 28 + -22p + 4p2 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), '2'. 2(14 + -11p + 2p2) = 0 Factor a trinomial. 2((2 + -1p)(7 + -2p)) = 0 Ignore the factor 2.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 '(7 + -2p)' equal to zero and attempt to solve: Simplifying 7 + -2p = 0 Solving 7 + -2p = 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 + -2p = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -2p = 0 + -7 -2p = 0 + -7 Combine like terms: 0 + -7 = -7 -2p = -7 Divide each side by '-2'. p = 3.5 Simplifying p = 3.5Solution
p = {2, 3.5}
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