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Simplifying p2 = -20 + -10p Solving p2 = -20 + -10p Solving for variable 'p'. Reorder the terms: 20 + 10p + p2 = -20 + -10p + 20 + 10p Reorder the terms: 20 + 10p + p2 = -20 + 20 + -10p + 10p Combine like terms: -20 + 20 = 0 20 + 10p + p2 = 0 + -10p + 10p 20 + 10p + p2 = -10p + 10p Combine like terms: -10p + 10p = 0 20 + 10p + p2 = 0 Begin completing the square. Move the constant term to the right: Add '-20' to each side of the equation. 20 + 10p + -20 + p2 = 0 + -20 Reorder the terms: 20 + -20 + 10p + p2 = 0 + -20 Combine like terms: 20 + -20 = 0 0 + 10p + p2 = 0 + -20 10p + p2 = 0 + -20 Combine like terms: 0 + -20 = -20 10p + p2 = -20 The p term is 10p. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10p + 25 + p2 = -20 + 25 Reorder the terms: 25 + 10p + p2 = -20 + 25 Combine like terms: -20 + 25 = 5 25 + 10p + p2 = 5 Factor a perfect square on the left side: (p + 5)(p + 5) = 5 Calculate the square root of the right side: 2.236067978 Break this problem into two subproblems by setting (p + 5) equal to 2.236067978 and -2.236067978.Subproblem 1
p + 5 = 2.236067978 Simplifying p + 5 = 2.236067978 Reorder the terms: 5 + p = 2.236067978 Solving 5 + p = 2.236067978 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + p = 2.236067978 + -5 Combine like terms: 5 + -5 = 0 0 + p = 2.236067978 + -5 p = 2.236067978 + -5 Combine like terms: 2.236067978 + -5 = -2.763932022 p = -2.763932022 Simplifying p = -2.763932022Subproblem 2
p + 5 = -2.236067978 Simplifying p + 5 = -2.236067978 Reorder the terms: 5 + p = -2.236067978 Solving 5 + p = -2.236067978 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + p = -2.236067978 + -5 Combine like terms: 5 + -5 = 0 0 + p = -2.236067978 + -5 p = -2.236067978 + -5 Combine like terms: -2.236067978 + -5 = -7.236067978 p = -7.236067978 Simplifying p = -7.236067978Solution
The solution to the problem is based on the solutions from the subproblems. p = {-2.763932022, -7.236067978}
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