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Simplifying -1p2 + 11p = -1 Reorder the terms: 11p + -1p2 = -1 Solving 11p + -1p2 = -1 Solving for variable 'p'. Reorder the terms: 1 + 11p + -1p2 = -1 + 1 Combine like terms: -1 + 1 = 0 1 + 11p + -1p2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -1 + -11p + p2 = 0 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 = 31.25 30.25 + -11p + p2 = 31.25 Factor a perfect square on the left side: (p + -5.5)(p + -5.5) = 31.25 Calculate the square root of the right side: 5.590169944 Break this problem into two subproblems by setting (p + -5.5) equal to 5.590169944 and -5.590169944.Subproblem 1
p + -5.5 = 5.590169944 Simplifying p + -5.5 = 5.590169944 Reorder the terms: -5.5 + p = 5.590169944 Solving -5.5 + p = 5.590169944 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 = 5.590169944 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + p = 5.590169944 + 5.5 p = 5.590169944 + 5.5 Combine like terms: 5.590169944 + 5.5 = 11.090169944 p = 11.090169944 Simplifying p = 11.090169944Subproblem 2
p + -5.5 = -5.590169944 Simplifying p + -5.5 = -5.590169944 Reorder the terms: -5.5 + p = -5.590169944 Solving -5.5 + p = -5.590169944 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 = -5.590169944 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + p = -5.590169944 + 5.5 p = -5.590169944 + 5.5 Combine like terms: -5.590169944 + 5.5 = -0.090169944 p = -0.090169944 Simplifying p = -0.090169944Solution
The solution to the problem is based on the solutions from the subproblems. p = {11.090169944, -0.090169944}
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