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Simplifying 15p2 + p = 14(3p + -1) Reorder the terms: p + 15p2 = 14(3p + -1) Reorder the terms: p + 15p2 = 14(-1 + 3p) p + 15p2 = (-1 * 14 + 3p * 14) p + 15p2 = (-14 + 42p) Solving p + 15p2 = -14 + 42p Solving for variable 'p'. Reorder the terms: 14 + p + -42p + 15p2 = -14 + 42p + 14 + -42p Combine like terms: p + -42p = -41p 14 + -41p + 15p2 = -14 + 42p + 14 + -42p Reorder the terms: 14 + -41p + 15p2 = -14 + 14 + 42p + -42p Combine like terms: -14 + 14 = 0 14 + -41p + 15p2 = 0 + 42p + -42p 14 + -41p + 15p2 = 42p + -42p Combine like terms: 42p + -42p = 0 14 + -41p + 15p2 = 0 Factor a trinomial. (2 + -5p)(7 + -3p) = 0Subproblem 1
Set the factor '(2 + -5p)' equal to zero and attempt to solve: Simplifying 2 + -5p = 0 Solving 2 + -5p = 0 Move all terms containing p to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -5p = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -5p = 0 + -2 -5p = 0 + -2 Combine like terms: 0 + -2 = -2 -5p = -2 Divide each side by '-5'. p = 0.4 Simplifying p = 0.4Subproblem 2
Set the factor '(7 + -3p)' equal to zero and attempt to solve: Simplifying 7 + -3p = 0 Solving 7 + -3p = 0 Move all terms containing p to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -3p = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -3p = 0 + -7 -3p = 0 + -7 Combine like terms: 0 + -7 = -7 -3p = -7 Divide each side by '-3'. p = 2.333333333 Simplifying p = 2.333333333Solution
p = {0.4, 2.333333333}
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