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Simplifying 11p2 + -15 = -7p Reorder the terms: -15 + 11p2 = -7p Solving -15 + 11p2 = -7p Solving for variable 'p'. Reorder the terms: -15 + 7p + 11p2 = -7p + 7p Combine like terms: -7p + 7p = 0 -15 + 7p + 11p2 = 0 Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -1.363636364 + 0.6363636364p + p2 = 0 Move the constant term to the right: Add '1.363636364' to each side of the equation. -1.363636364 + 0.6363636364p + 1.363636364 + p2 = 0 + 1.363636364 Reorder the terms: -1.363636364 + 1.363636364 + 0.6363636364p + p2 = 0 + 1.363636364 Combine like terms: -1.363636364 + 1.363636364 = 0.000000000 0.000000000 + 0.6363636364p + p2 = 0 + 1.363636364 0.6363636364p + p2 = 0 + 1.363636364 Combine like terms: 0 + 1.363636364 = 1.363636364 0.6363636364p + p2 = 1.363636364 The p term is 0.6363636364p. Take half its coefficient (0.3181818182). Square it (0.1012396694) and add it to both sides. Add '0.1012396694' to each side of the equation. 0.6363636364p + 0.1012396694 + p2 = 1.363636364 + 0.1012396694 Reorder the terms: 0.1012396694 + 0.6363636364p + p2 = 1.363636364 + 0.1012396694 Combine like terms: 1.363636364 + 0.1012396694 = 1.4648760334 0.1012396694 + 0.6363636364p + p2 = 1.4648760334 Factor a perfect square on the left side: (p + 0.3181818182)(p + 0.3181818182) = 1.4648760334 Calculate the square root of the right side: 1.210320632 Break this problem into two subproblems by setting (p + 0.3181818182) equal to 1.210320632 and -1.210320632.Subproblem 1
p + 0.3181818182 = 1.210320632 Simplifying p + 0.3181818182 = 1.210320632 Reorder the terms: 0.3181818182 + p = 1.210320632 Solving 0.3181818182 + p = 1.210320632 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-0.3181818182' to each side of the equation. 0.3181818182 + -0.3181818182 + p = 1.210320632 + -0.3181818182 Combine like terms: 0.3181818182 + -0.3181818182 = 0.0000000000 0.0000000000 + p = 1.210320632 + -0.3181818182 p = 1.210320632 + -0.3181818182 Combine like terms: 1.210320632 + -0.3181818182 = 0.8921388138 p = 0.8921388138 Simplifying p = 0.8921388138Subproblem 2
p + 0.3181818182 = -1.210320632 Simplifying p + 0.3181818182 = -1.210320632 Reorder the terms: 0.3181818182 + p = -1.210320632 Solving 0.3181818182 + p = -1.210320632 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-0.3181818182' to each side of the equation. 0.3181818182 + -0.3181818182 + p = -1.210320632 + -0.3181818182 Combine like terms: 0.3181818182 + -0.3181818182 = 0.0000000000 0.0000000000 + p = -1.210320632 + -0.3181818182 p = -1.210320632 + -0.3181818182 Combine like terms: -1.210320632 + -0.3181818182 = -1.5285024502 p = -1.5285024502 Simplifying p = -1.5285024502Solution
The solution to the problem is based on the solutions from the subproblems. p = {0.8921388138, -1.5285024502}
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