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Simplifying p2 + 8p + 7 = -6 Reorder the terms: 7 + 8p + p2 = -6 Solving 7 + 8p + p2 = -6 Solving for variable 'p'. Reorder the terms: 7 + 6 + 8p + p2 = -6 + 6 Combine like terms: 7 + 6 = 13 13 + 8p + p2 = -6 + 6 Combine like terms: -6 + 6 = 0 13 + 8p + p2 = 0 Begin completing the square. Move the constant term to the right: Add '-13' to each side of the equation. 13 + 8p + -13 + p2 = 0 + -13 Reorder the terms: 13 + -13 + 8p + p2 = 0 + -13 Combine like terms: 13 + -13 = 0 0 + 8p + p2 = 0 + -13 8p + p2 = 0 + -13 Combine like terms: 0 + -13 = -13 8p + p2 = -13 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 = -13 + 16 Reorder the terms: 16 + 8p + p2 = -13 + 16 Combine like terms: -13 + 16 = 3 16 + 8p + p2 = 3 Factor a perfect square on the left side: (p + 4)(p + 4) = 3 Calculate the square root of the right side: 1.732050808 Break this problem into two subproblems by setting (p + 4) equal to 1.732050808 and -1.732050808.Subproblem 1
p + 4 = 1.732050808 Simplifying p + 4 = 1.732050808 Reorder the terms: 4 + p = 1.732050808 Solving 4 + p = 1.732050808 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 = 1.732050808 + -4 Combine like terms: 4 + -4 = 0 0 + p = 1.732050808 + -4 p = 1.732050808 + -4 Combine like terms: 1.732050808 + -4 = -2.267949192 p = -2.267949192 Simplifying p = -2.267949192Subproblem 2
p + 4 = -1.732050808 Simplifying p + 4 = -1.732050808 Reorder the terms: 4 + p = -1.732050808 Solving 4 + p = -1.732050808 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 = -1.732050808 + -4 Combine like terms: 4 + -4 = 0 0 + p = -1.732050808 + -4 p = -1.732050808 + -4 Combine like terms: -1.732050808 + -4 = -5.732050808 p = -5.732050808 Simplifying p = -5.732050808Solution
The solution to the problem is based on the solutions from the subproblems. p = {-2.267949192, -5.732050808}
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