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Simplifying -1p2 + -11p = 11 Reorder the terms: -11p + -1p2 = 11 Solving -11p + -1p2 = 11 Solving for variable 'p'. Reorder the terms: -11 + -11p + -1p2 = 11 + -11 Combine like terms: 11 + -11 = 0 -11 + -11p + -1p2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(11 + 11p + p2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(11 + 11p + p2)' equal to zero and attempt to solve: Simplifying 11 + 11p + p2 = 0 Solving 11 + 11p + p2 = 0 Begin completing the square. Move the constant term to the right: Add '-11' to each side of the equation. 11 + 11p + -11 + p2 = 0 + -11 Reorder the terms: 11 + -11 + 11p + p2 = 0 + -11 Combine like terms: 11 + -11 = 0 0 + 11p + p2 = 0 + -11 11p + p2 = 0 + -11 Combine like terms: 0 + -11 = -11 11p + p2 = -11 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 = -11 + 30.25 Reorder the terms: 30.25 + 11p + p2 = -11 + 30.25 Combine like terms: -11 + 30.25 = 19.25 30.25 + 11p + p2 = 19.25 Factor a perfect square on the left side: (p + 5.5)(p + 5.5) = 19.25 Calculate the square root of the right side: 4.387482194 Break this problem into two subproblems by setting (p + 5.5) equal to 4.387482194 and -4.387482194.Subproblem 1
p + 5.5 = 4.387482194 Simplifying p + 5.5 = 4.387482194 Reorder the terms: 5.5 + p = 4.387482194 Solving 5.5 + p = 4.387482194 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 = 4.387482194 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + p = 4.387482194 + -5.5 p = 4.387482194 + -5.5 Combine like terms: 4.387482194 + -5.5 = -1.112517806 p = -1.112517806 Simplifying p = -1.112517806Subproblem 2
p + 5.5 = -4.387482194 Simplifying p + 5.5 = -4.387482194 Reorder the terms: 5.5 + p = -4.387482194 Solving 5.5 + p = -4.387482194 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 = -4.387482194 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + p = -4.387482194 + -5.5 p = -4.387482194 + -5.5 Combine like terms: -4.387482194 + -5.5 = -9.887482194 p = -9.887482194 Simplifying p = -9.887482194Solution
The solution to the problem is based on the solutions from the subproblems. p = {-1.112517806, -9.887482194}Solution
p = {-1.112517806, -9.887482194}
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