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Simplifying 4p2 = 4p + -1 Reorder the terms: 4p2 = -1 + 4p Solving 4p2 = -1 + 4p Solving for variable 'p'. Reorder the terms: 1 + -4p + 4p2 = -1 + 4p + 1 + -4p Reorder the terms: 1 + -4p + 4p2 = -1 + 1 + 4p + -4p Combine like terms: -1 + 1 = 0 1 + -4p + 4p2 = 0 + 4p + -4p 1 + -4p + 4p2 = 4p + -4p Combine like terms: 4p + -4p = 0 1 + -4p + 4p2 = 0 Factor a trinomial. (1 + -2p)(1 + -2p) = 0Subproblem 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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