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Simplifying p2 + 6p = 127 Reorder the terms: 6p + p2 = 127 Solving 6p + p2 = 127 Solving for variable 'p'. Reorder the terms: -127 + 6p + p2 = 127 + -127 Combine like terms: 127 + -127 = 0 -127 + 6p + p2 = 0 Begin completing the square. Move the constant term to the right: Add '127' to each side of the equation. -127 + 6p + 127 + p2 = 0 + 127 Reorder the terms: -127 + 127 + 6p + p2 = 0 + 127 Combine like terms: -127 + 127 = 0 0 + 6p + p2 = 0 + 127 6p + p2 = 0 + 127 Combine like terms: 0 + 127 = 127 6p + p2 = 127 The p term is 6p. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6p + 9 + p2 = 127 + 9 Reorder the terms: 9 + 6p + p2 = 127 + 9 Combine like terms: 127 + 9 = 136 9 + 6p + p2 = 136 Factor a perfect square on the left side: (p + 3)(p + 3) = 136 Calculate the square root of the right side: 11.66190379 Break this problem into two subproblems by setting (p + 3) equal to 11.66190379 and -11.66190379.Subproblem 1
p + 3 = 11.66190379 Simplifying p + 3 = 11.66190379 Reorder the terms: 3 + p = 11.66190379 Solving 3 + p = 11.66190379 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + p = 11.66190379 + -3 Combine like terms: 3 + -3 = 0 0 + p = 11.66190379 + -3 p = 11.66190379 + -3 Combine like terms: 11.66190379 + -3 = 8.66190379 p = 8.66190379 Simplifying p = 8.66190379Subproblem 2
p + 3 = -11.66190379 Simplifying p + 3 = -11.66190379 Reorder the terms: 3 + p = -11.66190379 Solving 3 + p = -11.66190379 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + p = -11.66190379 + -3 Combine like terms: 3 + -3 = 0 0 + p = -11.66190379 + -3 p = -11.66190379 + -3 Combine like terms: -11.66190379 + -3 = -14.66190379 p = -14.66190379 Simplifying p = -14.66190379Solution
The solution to the problem is based on the solutions from the subproblems. p = {8.66190379, -14.66190379}
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