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Simplifying 6p2 + -11p + -45 = 0 Reorder the terms: -45 + -11p + 6p2 = 0 Solving -45 + -11p + 6p2 = 0 Solving for variable 'p'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -7.5 + -1.833333333p + p2 = 0 Move the constant term to the right: Add '7.5' to each side of the equation. -7.5 + -1.833333333p + 7.5 + p2 = 0 + 7.5 Reorder the terms: -7.5 + 7.5 + -1.833333333p + p2 = 0 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + -1.833333333p + p2 = 0 + 7.5 -1.833333333p + p2 = 0 + 7.5 Combine like terms: 0 + 7.5 = 7.5 -1.833333333p + p2 = 7.5 The p term is -1.833333333p. Take half its coefficient (-0.9166666665). Square it (0.8402777775) and add it to both sides. Add '0.8402777775' to each side of the equation. -1.833333333p + 0.8402777775 + p2 = 7.5 + 0.8402777775 Reorder the terms: 0.8402777775 + -1.833333333p + p2 = 7.5 + 0.8402777775 Combine like terms: 7.5 + 0.8402777775 = 8.3402777775 0.8402777775 + -1.833333333p + p2 = 8.3402777775 Factor a perfect square on the left side: (p + -0.9166666665)(p + -0.9166666665) = 8.3402777775 Calculate the square root of the right side: 2.887953908 Break this problem into two subproblems by setting (p + -0.9166666665) equal to 2.887953908 and -2.887953908.Subproblem 1
p + -0.9166666665 = 2.887953908 Simplifying p + -0.9166666665 = 2.887953908 Reorder the terms: -0.9166666665 + p = 2.887953908 Solving -0.9166666665 + p = 2.887953908 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.9166666665' to each side of the equation. -0.9166666665 + 0.9166666665 + p = 2.887953908 + 0.9166666665 Combine like terms: -0.9166666665 + 0.9166666665 = 0.0000000000 0.0000000000 + p = 2.887953908 + 0.9166666665 p = 2.887953908 + 0.9166666665 Combine like terms: 2.887953908 + 0.9166666665 = 3.8046205745 p = 3.8046205745 Simplifying p = 3.8046205745Subproblem 2
p + -0.9166666665 = -2.887953908 Simplifying p + -0.9166666665 = -2.887953908 Reorder the terms: -0.9166666665 + p = -2.887953908 Solving -0.9166666665 + p = -2.887953908 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.9166666665' to each side of the equation. -0.9166666665 + 0.9166666665 + p = -2.887953908 + 0.9166666665 Combine like terms: -0.9166666665 + 0.9166666665 = 0.0000000000 0.0000000000 + p = -2.887953908 + 0.9166666665 p = -2.887953908 + 0.9166666665 Combine like terms: -2.887953908 + 0.9166666665 = -1.9712872415 p = -1.9712872415 Simplifying p = -1.9712872415Solution
The solution to the problem is based on the solutions from the subproblems. p = {3.8046205745, -1.9712872415}
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