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Simplifying -14p(2p + 1) = 14p + 7 Reorder the terms: -14p(1 + 2p) = 14p + 7 (1 * -14p + 2p * -14p) = 14p + 7 (-14p + -28p2) = 14p + 7 Reorder the terms: -14p + -28p2 = 7 + 14p Solving -14p + -28p2 = 7 + 14p Solving for variable 'p'. Reorder the terms: -7 + -14p + -14p + -28p2 = 7 + 14p + -7 + -14p Combine like terms: -14p + -14p = -28p -7 + -28p + -28p2 = 7 + 14p + -7 + -14p Reorder the terms: -7 + -28p + -28p2 = 7 + -7 + 14p + -14p Combine like terms: 7 + -7 = 0 -7 + -28p + -28p2 = 0 + 14p + -14p -7 + -28p + -28p2 = 14p + -14p Combine like terms: 14p + -14p = 0 -7 + -28p + -28p2 = 0 Factor out the Greatest Common Factor (GCF), '-7'. -7(1 + 4p + 4p2) = 0 Factor a trinomial. -7((1 + 2p)(1 + 2p)) = 0 Ignore the factor -7.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 '(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 = -0.5Solution
p = {-0.5, -0.5}
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