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Simplifying p2 + 11p = 10 Reorder the terms: 11p + p2 = 10 Solving 11p + p2 = 10 Solving for variable 'p'. Reorder the terms: -10 + 11p + p2 = 10 + -10 Combine like terms: 10 + -10 = 0 -10 + 11p + p2 = 0 Begin completing the square. Move the constant term to the right: Add '10' to each side of the equation. -10 + 11p + 10 + p2 = 0 + 10 Reorder the terms: -10 + 10 + 11p + p2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + 11p + p2 = 0 + 10 11p + p2 = 0 + 10 Combine like terms: 0 + 10 = 10 11p + p2 = 10 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 = 10 + 30.25 Reorder the terms: 30.25 + 11p + p2 = 10 + 30.25 Combine like terms: 10 + 30.25 = 40.25 30.25 + 11p + p2 = 40.25 Factor a perfect square on the left side: (p + 5.5)(p + 5.5) = 40.25 Calculate the square root of the right side: 6.34428877 Break this problem into two subproblems by setting (p + 5.5) equal to 6.34428877 and -6.34428877.Subproblem 1
p + 5.5 = 6.34428877 Simplifying p + 5.5 = 6.34428877 Reorder the terms: 5.5 + p = 6.34428877 Solving 5.5 + p = 6.34428877 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 = 6.34428877 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + p = 6.34428877 + -5.5 p = 6.34428877 + -5.5 Combine like terms: 6.34428877 + -5.5 = 0.84428877 p = 0.84428877 Simplifying p = 0.84428877Subproblem 2
p + 5.5 = -6.34428877 Simplifying p + 5.5 = -6.34428877 Reorder the terms: 5.5 + p = -6.34428877 Solving 5.5 + p = -6.34428877 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 = -6.34428877 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + p = -6.34428877 + -5.5 p = -6.34428877 + -5.5 Combine like terms: -6.34428877 + -5.5 = -11.84428877 p = -11.84428877 Simplifying p = -11.84428877Solution
The solution to the problem is based on the solutions from the subproblems. p = {0.84428877, -11.84428877}
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