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Simplifying p2 + -3000p + 350000 = 0 Reorder the terms: 350000 + -3000p + p2 = 0 Solving 350000 + -3000p + p2 = 0 Solving for variable 'p'. Begin completing the square. Move the constant term to the right: Add '-350000' to each side of the equation. 350000 + -3000p + -350000 + p2 = 0 + -350000 Reorder the terms: 350000 + -350000 + -3000p + p2 = 0 + -350000 Combine like terms: 350000 + -350000 = 0 0 + -3000p + p2 = 0 + -350000 -3000p + p2 = 0 + -350000 Combine like terms: 0 + -350000 = -350000 -3000p + p2 = -350000 The p term is -3000p. Take half its coefficient (-1500). Square it (2250000) and add it to both sides. Add '2250000' to each side of the equation. -3000p + 2250000 + p2 = -350000 + 2250000 Reorder the terms: 2250000 + -3000p + p2 = -350000 + 2250000 Combine like terms: -350000 + 2250000 = 1900000 2250000 + -3000p + p2 = 1900000 Factor a perfect square on the left side: (p + -1500)(p + -1500) = 1900000 Calculate the square root of the right side: 1378.404875209 Break this problem into two subproblems by setting (p + -1500) equal to 1378.404875209 and -1378.404875209.Subproblem 1
p + -1500 = 1378.404875209 Simplifying p + -1500 = 1378.404875209 Reorder the terms: -1500 + p = 1378.404875209 Solving -1500 + p = 1378.404875209 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '1500' to each side of the equation. -1500 + 1500 + p = 1378.404875209 + 1500 Combine like terms: -1500 + 1500 = 0 0 + p = 1378.404875209 + 1500 p = 1378.404875209 + 1500 Combine like terms: 1378.404875209 + 1500 = 2878.404875209 p = 2878.404875209 Simplifying p = 2878.404875209Subproblem 2
p + -1500 = -1378.404875209 Simplifying p + -1500 = -1378.404875209 Reorder the terms: -1500 + p = -1378.404875209 Solving -1500 + p = -1378.404875209 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '1500' to each side of the equation. -1500 + 1500 + p = -1378.404875209 + 1500 Combine like terms: -1500 + 1500 = 0 0 + p = -1378.404875209 + 1500 p = -1378.404875209 + 1500 Combine like terms: -1378.404875209 + 1500 = 121.595124791 p = 121.595124791 Simplifying p = 121.595124791Solution
The solution to the problem is based on the solutions from the subproblems. p = {2878.404875209, 121.595124791}
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