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Simplifying (5p + -1)(25p + 5p + 1) = 0 Reorder the terms: (-1 + 5p)(25p + 5p + 1) = 0 Reorder the terms: (-1 + 5p)(1 + 25p + 5p) = 0 Combine like terms: 25p + 5p = 30p (-1 + 5p)(1 + 30p) = 0 Multiply (-1 + 5p) * (1 + 30p) (-1(1 + 30p) + 5p * (1 + 30p)) = 0 ((1 * -1 + 30p * -1) + 5p * (1 + 30p)) = 0 ((-1 + -30p) + 5p * (1 + 30p)) = 0 (-1 + -30p + (1 * 5p + 30p * 5p)) = 0 (-1 + -30p + (5p + 150p2)) = 0 Combine like terms: -30p + 5p = -25p (-1 + -25p + 150p2) = 0 Solving -1 + -25p + 150p2 = 0 Solving for variable 'p'. Factor a trinomial. (-1 + -30p)(1 + -5p) = 0Subproblem 1
Set the factor '(-1 + -30p)' equal to zero and attempt to solve: Simplifying -1 + -30p = 0 Solving -1 + -30p = 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 + -30p = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -30p = 0 + 1 -30p = 0 + 1 Combine like terms: 0 + 1 = 1 -30p = 1 Divide each side by '-30'. p = -0.03333333333 Simplifying p = -0.03333333333Subproblem 2
Set the factor '(1 + -5p)' equal to zero and attempt to solve: Simplifying 1 + -5p = 0 Solving 1 + -5p = 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 + -5p = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -5p = 0 + -1 -5p = 0 + -1 Combine like terms: 0 + -1 = -1 -5p = -1 Divide each side by '-5'. p = 0.2 Simplifying p = 0.2Solution
p = {-0.03333333333, 0.2}
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