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Simplifying 7p(p + -2) + 2(p + 4) = 3 Reorder the terms: 7p(-2 + p) + 2(p + 4) = 3 (-2 * 7p + p * 7p) + 2(p + 4) = 3 (-14p + 7p2) + 2(p + 4) = 3 Reorder the terms: -14p + 7p2 + 2(4 + p) = 3 -14p + 7p2 + (4 * 2 + p * 2) = 3 -14p + 7p2 + (8 + 2p) = 3 Reorder the terms: 8 + -14p + 2p + 7p2 = 3 Combine like terms: -14p + 2p = -12p 8 + -12p + 7p2 = 3 Solving 8 + -12p + 7p2 = 3 Solving for variable 'p'. Reorder the terms: 8 + -3 + -12p + 7p2 = 3 + -3 Combine like terms: 8 + -3 = 5 5 + -12p + 7p2 = 3 + -3 Combine like terms: 3 + -3 = 0 5 + -12p + 7p2 = 0 Factor a trinomial. (5 + -7p)(1 + -1p) = 0Subproblem 1
Set the factor '(5 + -7p)' equal to zero and attempt to solve: Simplifying 5 + -7p = 0 Solving 5 + -7p = 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 + -7p = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -7p = 0 + -5 -7p = 0 + -5 Combine like terms: 0 + -5 = -5 -7p = -5 Divide each side by '-7'. p = 0.7142857143 Simplifying p = 0.7142857143Subproblem 2
Set the factor '(1 + -1p)' equal to zero and attempt to solve: Simplifying 1 + -1p = 0 Solving 1 + -1p = 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 + -1p = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1p = 0 + -1 -1p = 0 + -1 Combine like terms: 0 + -1 = -1 -1p = -1 Divide each side by '-1'. p = 1 Simplifying p = 1Solution
p = {0.7142857143, 1}
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