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Simplifying p2 + -11p + -5 = 0 Reorder the terms: -5 + -11p + p2 = 0 Solving -5 + -11p + p2 = 0 Solving for variable 'p'. Begin completing the square. Move the constant term to the right: Add '5' to each side of the equation. -5 + -11p + 5 + p2 = 0 + 5 Reorder the terms: -5 + 5 + -11p + p2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -11p + p2 = 0 + 5 -11p + p2 = 0 + 5 Combine like terms: 0 + 5 = 5 -11p + p2 = 5 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 = 5 + 30.25 Reorder the terms: 30.25 + -11p + p2 = 5 + 30.25 Combine like terms: 5 + 30.25 = 35.25 30.25 + -11p + p2 = 35.25 Factor a perfect square on the left side: (p + -5.5)(p + -5.5) = 35.25 Calculate the square root of the right side: 5.937171044 Break this problem into two subproblems by setting (p + -5.5) equal to 5.937171044 and -5.937171044.Subproblem 1
p + -5.5 = 5.937171044 Simplifying p + -5.5 = 5.937171044 Reorder the terms: -5.5 + p = 5.937171044 Solving -5.5 + p = 5.937171044 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 = 5.937171044 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + p = 5.937171044 + 5.5 p = 5.937171044 + 5.5 Combine like terms: 5.937171044 + 5.5 = 11.437171044 p = 11.437171044 Simplifying p = 11.437171044Subproblem 2
p + -5.5 = -5.937171044 Simplifying p + -5.5 = -5.937171044 Reorder the terms: -5.5 + p = -5.937171044 Solving -5.5 + p = -5.937171044 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 = -5.937171044 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + p = -5.937171044 + 5.5 p = -5.937171044 + 5.5 Combine like terms: -5.937171044 + 5.5 = -0.437171044 p = -0.437171044 Simplifying p = -0.437171044Solution
The solution to the problem is based on the solutions from the subproblems. p = {11.437171044, -0.437171044}
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