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Simplifying p2 + 11p = 18 Reorder the terms: 11p + p2 = 18 Solving 11p + p2 = 18 Solving for variable 'p'. Reorder the terms: -18 + 11p + p2 = 18 + -18 Combine like terms: 18 + -18 = 0 -18 + 11p + p2 = 0 Begin completing the square. Move the constant term to the right: Add '18' to each side of the equation. -18 + 11p + 18 + p2 = 0 + 18 Reorder the terms: -18 + 18 + 11p + p2 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + 11p + p2 = 0 + 18 11p + p2 = 0 + 18 Combine like terms: 0 + 18 = 18 11p + p2 = 18 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 = 18 + 30.25 Reorder the terms: 30.25 + 11p + p2 = 18 + 30.25 Combine like terms: 18 + 30.25 = 48.25 30.25 + 11p + p2 = 48.25 Factor a perfect square on the left side: (p + 5.5)(p + 5.5) = 48.25 Calculate the square root of the right side: 6.946221995 Break this problem into two subproblems by setting (p + 5.5) equal to 6.946221995 and -6.946221995.Subproblem 1
p + 5.5 = 6.946221995 Simplifying p + 5.5 = 6.946221995 Reorder the terms: 5.5 + p = 6.946221995 Solving 5.5 + p = 6.946221995 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 = 6.946221995 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + p = 6.946221995 + -5.5 p = 6.946221995 + -5.5 Combine like terms: 6.946221995 + -5.5 = 1.446221995 p = 1.446221995 Simplifying p = 1.446221995Subproblem 2
p + 5.5 = -6.946221995 Simplifying p + 5.5 = -6.946221995 Reorder the terms: 5.5 + p = -6.946221995 Solving 5.5 + p = -6.946221995 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 = -6.946221995 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + p = -6.946221995 + -5.5 p = -6.946221995 + -5.5 Combine like terms: -6.946221995 + -5.5 = -12.446221995 p = -12.446221995 Simplifying p = -12.446221995Solution
The solution to the problem is based on the solutions from the subproblems. p = {1.446221995, -12.446221995}
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