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Simplifying -2p2 + -10p + 11 = 0 Reorder the terms: 11 + -10p + -2p2 = 0 Solving 11 + -10p + -2p2 = 0 Solving for variable 'p'. Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -5.5 + 5p + p2 = 0 Move the constant term to the right: Add '5.5' to each side of the equation. -5.5 + 5p + 5.5 + p2 = 0 + 5.5 Reorder the terms: -5.5 + 5.5 + 5p + p2 = 0 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + 5p + p2 = 0 + 5.5 5p + p2 = 0 + 5.5 Combine like terms: 0 + 5.5 = 5.5 5p + p2 = 5.5 The p term is 5p. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5p + 6.25 + p2 = 5.5 + 6.25 Reorder the terms: 6.25 + 5p + p2 = 5.5 + 6.25 Combine like terms: 5.5 + 6.25 = 11.75 6.25 + 5p + p2 = 11.75 Factor a perfect square on the left side: (p + 2.5)(p + 2.5) = 11.75 Calculate the square root of the right side: 3.4278273 Break this problem into two subproblems by setting (p + 2.5) equal to 3.4278273 and -3.4278273.Subproblem 1
p + 2.5 = 3.4278273 Simplifying p + 2.5 = 3.4278273 Reorder the terms: 2.5 + p = 3.4278273 Solving 2.5 + p = 3.4278273 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + p = 3.4278273 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + p = 3.4278273 + -2.5 p = 3.4278273 + -2.5 Combine like terms: 3.4278273 + -2.5 = 0.9278273 p = 0.9278273 Simplifying p = 0.9278273Subproblem 2
p + 2.5 = -3.4278273 Simplifying p + 2.5 = -3.4278273 Reorder the terms: 2.5 + p = -3.4278273 Solving 2.5 + p = -3.4278273 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + p = -3.4278273 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + p = -3.4278273 + -2.5 p = -3.4278273 + -2.5 Combine like terms: -3.4278273 + -2.5 = -5.9278273 p = -5.9278273 Simplifying p = -5.9278273Solution
The solution to the problem is based on the solutions from the subproblems. p = {0.9278273, -5.9278273}
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