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Simplifying p2 + 8p = 25 Reorder the terms: 8p + p2 = 25 Solving 8p + p2 = 25 Solving for variable 'p'. Reorder the terms: -25 + 8p + p2 = 25 + -25 Combine like terms: 25 + -25 = 0 -25 + 8p + p2 = 0 Begin completing the square. Move the constant term to the right: Add '25' to each side of the equation. -25 + 8p + 25 + p2 = 0 + 25 Reorder the terms: -25 + 25 + 8p + p2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + 8p + p2 = 0 + 25 8p + p2 = 0 + 25 Combine like terms: 0 + 25 = 25 8p + p2 = 25 The p term is 8p. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8p + 16 + p2 = 25 + 16 Reorder the terms: 16 + 8p + p2 = 25 + 16 Combine like terms: 25 + 16 = 41 16 + 8p + p2 = 41 Factor a perfect square on the left side: (p + 4)(p + 4) = 41 Calculate the square root of the right side: 6.403124237 Break this problem into two subproblems by setting (p + 4) equal to 6.403124237 and -6.403124237.Subproblem 1
p + 4 = 6.403124237 Simplifying p + 4 = 6.403124237 Reorder the terms: 4 + p = 6.403124237 Solving 4 + p = 6.403124237 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + p = 6.403124237 + -4 Combine like terms: 4 + -4 = 0 0 + p = 6.403124237 + -4 p = 6.403124237 + -4 Combine like terms: 6.403124237 + -4 = 2.403124237 p = 2.403124237 Simplifying p = 2.403124237Subproblem 2
p + 4 = -6.403124237 Simplifying p + 4 = -6.403124237 Reorder the terms: 4 + p = -6.403124237 Solving 4 + p = -6.403124237 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + p = -6.403124237 + -4 Combine like terms: 4 + -4 = 0 0 + p = -6.403124237 + -4 p = -6.403124237 + -4 Combine like terms: -6.403124237 + -4 = -10.403124237 p = -10.403124237 Simplifying p = -10.403124237Solution
The solution to the problem is based on the solutions from the subproblems. p = {2.403124237, -10.403124237}
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