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Simplifying p2 + -11p + 1 = 0 Reorder the terms: 1 + -11p + p2 = 0 Solving 1 + -11p + p2 = 0 Solving for variable 'p'. Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + -11p + -1 + p2 = 0 + -1 Reorder the terms: 1 + -1 + -11p + p2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -11p + p2 = 0 + -1 -11p + p2 = 0 + -1 Combine like terms: 0 + -1 = -1 -11p + p2 = -1 The p term is -11p. Take half its coefficient (-5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. -11p + 30.25 + p2 = -1 + 30.25 Reorder the terms: 30.25 + -11p + p2 = -1 + 30.25 Combine like terms: -1 + 30.25 = 29.25 30.25 + -11p + p2 = 29.25 Factor a perfect square on the left side: (p + -5.5)(p + -5.5) = 29.25 Calculate the square root of the right side: 5.408326913 Break this problem into two subproblems by setting (p + -5.5) equal to 5.408326913 and -5.408326913.Subproblem 1
p + -5.5 = 5.408326913 Simplifying p + -5.5 = 5.408326913 Reorder the terms: -5.5 + p = 5.408326913 Solving -5.5 + p = 5.408326913 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + p = 5.408326913 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + p = 5.408326913 + 5.5 p = 5.408326913 + 5.5 Combine like terms: 5.408326913 + 5.5 = 10.908326913 p = 10.908326913 Simplifying p = 10.908326913Subproblem 2
p + -5.5 = -5.408326913 Simplifying p + -5.5 = -5.408326913 Reorder the terms: -5.5 + p = -5.408326913 Solving -5.5 + p = -5.408326913 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + p = -5.408326913 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + p = -5.408326913 + 5.5 p = -5.408326913 + 5.5 Combine like terms: -5.408326913 + 5.5 = 0.091673087 p = 0.091673087 Simplifying p = 0.091673087Solution
The solution to the problem is based on the solutions from the subproblems. p = {10.908326913, 0.091673087}
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