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Simplifying p2 + -2000p + 300000 = 0 Reorder the terms: 300000 + -2000p + p2 = 0 Solving 300000 + -2000p + p2 = 0 Solving for variable 'p'. Begin completing the square. Move the constant term to the right: Add '-300000' to each side of the equation. 300000 + -2000p + -300000 + p2 = 0 + -300000 Reorder the terms: 300000 + -300000 + -2000p + p2 = 0 + -300000 Combine like terms: 300000 + -300000 = 0 0 + -2000p + p2 = 0 + -300000 -2000p + p2 = 0 + -300000 Combine like terms: 0 + -300000 = -300000 -2000p + p2 = -300000 The p term is -2000p. Take half its coefficient (-1000). Square it (1000000) and add it to both sides. Add '1000000' to each side of the equation. -2000p + 1000000 + p2 = -300000 + 1000000 Reorder the terms: 1000000 + -2000p + p2 = -300000 + 1000000 Combine like terms: -300000 + 1000000 = 700000 1000000 + -2000p + p2 = 700000 Factor a perfect square on the left side: (p + -1000)(p + -1000) = 700000 Calculate the square root of the right side: 836.660026534 Break this problem into two subproblems by setting (p + -1000) equal to 836.660026534 and -836.660026534.Subproblem 1
p + -1000 = 836.660026534 Simplifying p + -1000 = 836.660026534 Reorder the terms: -1000 + p = 836.660026534 Solving -1000 + p = 836.660026534 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '1000' to each side of the equation. -1000 + 1000 + p = 836.660026534 + 1000 Combine like terms: -1000 + 1000 = 0 0 + p = 836.660026534 + 1000 p = 836.660026534 + 1000 Combine like terms: 836.660026534 + 1000 = 1836.660026534 p = 1836.660026534 Simplifying p = 1836.660026534Subproblem 2
p + -1000 = -836.660026534 Simplifying p + -1000 = -836.660026534 Reorder the terms: -1000 + p = -836.660026534 Solving -1000 + p = -836.660026534 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '1000' to each side of the equation. -1000 + 1000 + p = -836.660026534 + 1000 Combine like terms: -1000 + 1000 = 0 0 + p = -836.660026534 + 1000 p = -836.660026534 + 1000 Combine like terms: -836.660026534 + 1000 = 163.339973466 p = 163.339973466 Simplifying p = 163.339973466Solution
The solution to the problem is based on the solutions from the subproblems. p = {1836.660026534, 163.339973466}
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