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Simplifying 11p2 + -1 = -8p Reorder the terms: -1 + 11p2 = -8p Solving -1 + 11p2 = -8p Solving for variable 'p'. Reorder the terms: -1 + 8p + 11p2 = -8p + 8p Combine like terms: -8p + 8p = 0 -1 + 8p + 11p2 = 0 Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -0.09090909091 + 0.7272727273p + p2 = 0 Move the constant term to the right: Add '0.09090909091' to each side of the equation. -0.09090909091 + 0.7272727273p + 0.09090909091 + p2 = 0 + 0.09090909091 Reorder the terms: -0.09090909091 + 0.09090909091 + 0.7272727273p + p2 = 0 + 0.09090909091 Combine like terms: -0.09090909091 + 0.09090909091 = 0.00000000000 0.00000000000 + 0.7272727273p + p2 = 0 + 0.09090909091 0.7272727273p + p2 = 0 + 0.09090909091 Combine like terms: 0 + 0.09090909091 = 0.09090909091 0.7272727273p + p2 = 0.09090909091 The p term is 0.7272727273p. Take half its coefficient (0.3636363637). Square it (0.1322314050) and add it to both sides. Add '0.1322314050' to each side of the equation. 0.7272727273p + 0.1322314050 + p2 = 0.09090909091 + 0.1322314050 Reorder the terms: 0.1322314050 + 0.7272727273p + p2 = 0.09090909091 + 0.1322314050 Combine like terms: 0.09090909091 + 0.1322314050 = 0.22314049591 0.1322314050 + 0.7272727273p + p2 = 0.22314049591 Factor a perfect square on the left side: (p + 0.3636363637)(p + 0.3636363637) = 0.22314049591 Calculate the square root of the right side: 0.472377493 Break this problem into two subproblems by setting (p + 0.3636363637) equal to 0.472377493 and -0.472377493.Subproblem 1
p + 0.3636363637 = 0.472377493 Simplifying p + 0.3636363637 = 0.472377493 Reorder the terms: 0.3636363637 + p = 0.472377493 Solving 0.3636363637 + p = 0.472377493 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-0.3636363637' to each side of the equation. 0.3636363637 + -0.3636363637 + p = 0.472377493 + -0.3636363637 Combine like terms: 0.3636363637 + -0.3636363637 = 0.0000000000 0.0000000000 + p = 0.472377493 + -0.3636363637 p = 0.472377493 + -0.3636363637 Combine like terms: 0.472377493 + -0.3636363637 = 0.1087411293 p = 0.1087411293 Simplifying p = 0.1087411293Subproblem 2
p + 0.3636363637 = -0.472377493 Simplifying p + 0.3636363637 = -0.472377493 Reorder the terms: 0.3636363637 + p = -0.472377493 Solving 0.3636363637 + p = -0.472377493 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-0.3636363637' to each side of the equation. 0.3636363637 + -0.3636363637 + p = -0.472377493 + -0.3636363637 Combine like terms: 0.3636363637 + -0.3636363637 = 0.0000000000 0.0000000000 + p = -0.472377493 + -0.3636363637 p = -0.472377493 + -0.3636363637 Combine like terms: -0.472377493 + -0.3636363637 = -0.8360138567 p = -0.8360138567 Simplifying p = -0.8360138567Solution
The solution to the problem is based on the solutions from the subproblems. p = {0.1087411293, -0.8360138567}
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