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Simplifying -2p2 + 6000p = 800000 Reorder the terms: 6000p + -2p2 = 800000 Solving 6000p + -2p2 = 800000 Solving for variable 'p'. Reorder the terms: -800000 + 6000p + -2p2 = 800000 + -800000 Combine like terms: 800000 + -800000 = 0 -800000 + 6000p + -2p2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-400000 + 3000p + -1p2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-400000 + 3000p + -1p2)' equal to zero and attempt to solve: Simplifying -400000 + 3000p + -1p2 = 0 Solving -400000 + 3000p + -1p2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 400000 + -3000p + p2 = 0 Move the constant term to the right: Add '-400000' to each side of the equation. 400000 + -3000p + -400000 + p2 = 0 + -400000 Reorder the terms: 400000 + -400000 + -3000p + p2 = 0 + -400000 Combine like terms: 400000 + -400000 = 0 0 + -3000p + p2 = 0 + -400000 -3000p + p2 = 0 + -400000 Combine like terms: 0 + -400000 = -400000 -3000p + p2 = -400000 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 = -400000 + 2250000 Reorder the terms: 2250000 + -3000p + p2 = -400000 + 2250000 Combine like terms: -400000 + 2250000 = 1850000 2250000 + -3000p + p2 = 1850000 Factor a perfect square on the left side: (p + -1500)(p + -1500) = 1850000 Calculate the square root of the right side: 1360.147050874 Break this problem into two subproblems by setting (p + -1500) equal to 1360.147050874 and -1360.147050874.Subproblem 1
p + -1500 = 1360.147050874 Simplifying p + -1500 = 1360.147050874 Reorder the terms: -1500 + p = 1360.147050874 Solving -1500 + p = 1360.147050874 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 = 1360.147050874 + 1500 Combine like terms: -1500 + 1500 = 0 0 + p = 1360.147050874 + 1500 p = 1360.147050874 + 1500 Combine like terms: 1360.147050874 + 1500 = 2860.147050874 p = 2860.147050874 Simplifying p = 2860.147050874Subproblem 2
p + -1500 = -1360.147050874 Simplifying p + -1500 = -1360.147050874 Reorder the terms: -1500 + p = -1360.147050874 Solving -1500 + p = -1360.147050874 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 = -1360.147050874 + 1500 Combine like terms: -1500 + 1500 = 0 0 + p = -1360.147050874 + 1500 p = -1360.147050874 + 1500 Combine like terms: -1360.147050874 + 1500 = 139.852949126 p = 139.852949126 Simplifying p = 139.852949126Solution
The solution to the problem is based on the solutions from the subproblems. p = {2860.147050874, 139.852949126}Solution
p = {2860.147050874, 139.852949126}
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