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Simplifying 12.5p + -1(2 + p) * p = 2.5 Reorder the terms for easier multiplication: 12.5p + -1p(2 + p) = 2.5 12.5p + (2 * -1p + p * -1p) = 2.5 12.5p + (-2p + -1p2) = 2.5 Combine like terms: 12.5p + -2p = 10.5p 10.5p + -1p2 = 2.5 Solving 10.5p + -1p2 = 2.5 Solving for variable 'p'. Reorder the terms: -2.5 + 10.5p + -1p2 = 2.5 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 -2.5 + 10.5p + -1p2 = 0.0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 2.5 + -10.5p + p2 = 0.0 Move the constant term to the right: Add '-2.5' to each side of the equation. 2.5 + -10.5p + -2.5 + p2 = 0.0 + -2.5 Reorder the terms: 2.5 + -2.5 + -10.5p + p2 = 0.0 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + -10.5p + p2 = 0.0 + -2.5 -10.5p + p2 = 0.0 + -2.5 Combine like terms: 0.0 + -2.5 = -2.5 -10.5p + p2 = -2.5 The p term is -10.5p. Take half its coefficient (-5.25). Square it (27.5625) and add it to both sides. Add '27.5625' to each side of the equation. -10.5p + 27.5625 + p2 = -2.5 + 27.5625 Reorder the terms: 27.5625 + -10.5p + p2 = -2.5 + 27.5625 Combine like terms: -2.5 + 27.5625 = 25.0625 27.5625 + -10.5p + p2 = 25.0625 Factor a perfect square on the left side: (p + -5.25)(p + -5.25) = 25.0625 Calculate the square root of the right side: 5.006246099 Break this problem into two subproblems by setting (p + -5.25) equal to 5.006246099 and -5.006246099.Subproblem 1
p + -5.25 = 5.006246099 Simplifying p + -5.25 = 5.006246099 Reorder the terms: -5.25 + p = 5.006246099 Solving -5.25 + p = 5.006246099 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '5.25' to each side of the equation. -5.25 + 5.25 + p = 5.006246099 + 5.25 Combine like terms: -5.25 + 5.25 = 0.00 0.00 + p = 5.006246099 + 5.25 p = 5.006246099 + 5.25 Combine like terms: 5.006246099 + 5.25 = 10.256246099 p = 10.256246099 Simplifying p = 10.256246099Subproblem 2
p + -5.25 = -5.006246099 Simplifying p + -5.25 = -5.006246099 Reorder the terms: -5.25 + p = -5.006246099 Solving -5.25 + p = -5.006246099 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '5.25' to each side of the equation. -5.25 + 5.25 + p = -5.006246099 + 5.25 Combine like terms: -5.25 + 5.25 = 0.00 0.00 + p = -5.006246099 + 5.25 p = -5.006246099 + 5.25 Combine like terms: -5.006246099 + 5.25 = 0.243753901 p = 0.243753901 Simplifying p = 0.243753901Solution
The solution to the problem is based on the solutions from the subproblems. p = {10.256246099, 0.243753901}
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