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Simplifying 5 + -1p(8 + -1p) = 0 5 + (8 * -1p + -1p * -1p) = 0 5 + (-8p + 1p2) = 0 Solving 5 + -8p + 1p2 = 0 Solving for variable 'p'. Begin completing the square. Move the constant term to the right: Add '-5' to each side of the equation. 5 + -8p + -5 + p2 = 0 + -5 Reorder the terms: 5 + -5 + -8p + p2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -8p + p2 = 0 + -5 -8p + p2 = 0 + -5 Combine like terms: 0 + -5 = -5 -8p + p2 = -5 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 = -5 + 16 Reorder the terms: 16 + -8p + p2 = -5 + 16 Combine like terms: -5 + 16 = 11 16 + -8p + p2 = 11 Factor a perfect square on the left side: (p + -4)(p + -4) = 11 Calculate the square root of the right side: 3.31662479 Break this problem into two subproblems by setting (p + -4) equal to 3.31662479 and -3.31662479.Subproblem 1
p + -4 = 3.31662479 Simplifying p + -4 = 3.31662479 Reorder the terms: -4 + p = 3.31662479 Solving -4 + p = 3.31662479 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 = 3.31662479 + 4 Combine like terms: -4 + 4 = 0 0 + p = 3.31662479 + 4 p = 3.31662479 + 4 Combine like terms: 3.31662479 + 4 = 7.31662479 p = 7.31662479 Simplifying p = 7.31662479Subproblem 2
p + -4 = -3.31662479 Simplifying p + -4 = -3.31662479 Reorder the terms: -4 + p = -3.31662479 Solving -4 + p = -3.31662479 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 = -3.31662479 + 4 Combine like terms: -4 + 4 = 0 0 + p = -3.31662479 + 4 p = -3.31662479 + 4 Combine like terms: -3.31662479 + 4 = 0.68337521 p = 0.68337521 Simplifying p = 0.68337521Solution
The solution to the problem is based on the solutions from the subproblems. p = {7.31662479, 0.68337521}
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