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Simplifying (4p + -1)(4p + -1) = 0 Reorder the terms: (-1 + 4p)(4p + -1) = 0 Reorder the terms: (-1 + 4p)(-1 + 4p) = 0 Multiply (-1 + 4p) * (-1 + 4p) (-1(-1 + 4p) + 4p * (-1 + 4p)) = 0 ((-1 * -1 + 4p * -1) + 4p * (-1 + 4p)) = 0 ((1 + -4p) + 4p * (-1 + 4p)) = 0 (1 + -4p + (-1 * 4p + 4p * 4p)) = 0 (1 + -4p + (-4p + 16p2)) = 0 Combine like terms: -4p + -4p = -8p (1 + -8p + 16p2) = 0 Solving 1 + -8p + 16p2 = 0 Solving for variable 'p'. Factor a trinomial. (1 + -4p)(1 + -4p) = 0Subproblem 1
Set the factor '(1 + -4p)' equal to zero and attempt to solve: Simplifying 1 + -4p = 0 Solving 1 + -4p = 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 + -4p = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -4p = 0 + -1 -4p = 0 + -1 Combine like terms: 0 + -1 = -1 -4p = -1 Divide each side by '-4'. p = 0.25 Simplifying p = 0.25Subproblem 2
Set the factor '(1 + -4p)' equal to zero and attempt to solve: Simplifying 1 + -4p = 0 Solving 1 + -4p = 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 + -4p = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -4p = 0 + -1 -4p = 0 + -1 Combine like terms: 0 + -1 = -1 -4p = -1 Divide each side by '-4'. p = 0.25 Simplifying p = 0.25Solution
p = {0.25, 0.25}
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