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Simplifying p2 + -17p + -39 = 0 Reorder the terms: -39 + -17p + p2 = 0 Solving -39 + -17p + p2 = 0 Solving for variable 'p'. Begin completing the square. Move the constant term to the right: Add '39' to each side of the equation. -39 + -17p + 39 + p2 = 0 + 39 Reorder the terms: -39 + 39 + -17p + p2 = 0 + 39 Combine like terms: -39 + 39 = 0 0 + -17p + p2 = 0 + 39 -17p + p2 = 0 + 39 Combine like terms: 0 + 39 = 39 -17p + p2 = 39 The p term is -17p. Take half its coefficient (-8.5). Square it (72.25) and add it to both sides. Add '72.25' to each side of the equation. -17p + 72.25 + p2 = 39 + 72.25 Reorder the terms: 72.25 + -17p + p2 = 39 + 72.25 Combine like terms: 39 + 72.25 = 111.25 72.25 + -17p + p2 = 111.25 Factor a perfect square on the left side: (p + -8.5)(p + -8.5) = 111.25 Calculate the square root of the right side: 10.547511555 Break this problem into two subproblems by setting (p + -8.5) equal to 10.547511555 and -10.547511555.Subproblem 1
p + -8.5 = 10.547511555 Simplifying p + -8.5 = 10.547511555 Reorder the terms: -8.5 + p = 10.547511555 Solving -8.5 + p = 10.547511555 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + p = 10.547511555 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + p = 10.547511555 + 8.5 p = 10.547511555 + 8.5 Combine like terms: 10.547511555 + 8.5 = 19.047511555 p = 19.047511555 Simplifying p = 19.047511555Subproblem 2
p + -8.5 = -10.547511555 Simplifying p + -8.5 = -10.547511555 Reorder the terms: -8.5 + p = -10.547511555 Solving -8.5 + p = -10.547511555 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + p = -10.547511555 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + p = -10.547511555 + 8.5 p = -10.547511555 + 8.5 Combine like terms: -10.547511555 + 8.5 = -2.047511555 p = -2.047511555 Simplifying p = -2.047511555Solution
The solution to the problem is based on the solutions from the subproblems. p = {19.047511555, -2.047511555}
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