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Simplifying 12.5x = 50000 + 100x + -0.05x2 Solving 12.5x = 50000 + 100x + -0.05x2 Solving for variable 'x'. Reorder the terms: -50000 + 12.5x + -100x + 0.05x2 = 50000 + 100x + -0.05x2 + -50000 + -100x + 0.05x2 Combine like terms: 12.5x + -100x = -87.5x -50000 + -87.5x + 0.05x2 = 50000 + 100x + -0.05x2 + -50000 + -100x + 0.05x2 Reorder the terms: -50000 + -87.5x + 0.05x2 = 50000 + -50000 + 100x + -100x + -0.05x2 + 0.05x2 Combine like terms: 50000 + -50000 = 0 -50000 + -87.5x + 0.05x2 = 0 + 100x + -100x + -0.05x2 + 0.05x2 -50000 + -87.5x + 0.05x2 = 100x + -100x + -0.05x2 + 0.05x2 Combine like terms: 100x + -100x = 0 -50000 + -87.5x + 0.05x2 = 0 + -0.05x2 + 0.05x2 -50000 + -87.5x + 0.05x2 = -0.05x2 + 0.05x2 Combine like terms: -0.05x2 + 0.05x2 = 0.00 -50000 + -87.5x + 0.05x2 = 0.00 Begin completing the square. Divide all terms by 0.05 the coefficient of the squared term: Divide each side by '0.05'. -1000000 + -1750x + x2 = 0 Move the constant term to the right: Add '1000000' to each side of the equation. -1000000 + -1750x + 1000000 + x2 = 0 + 1000000 Reorder the terms: -1000000 + 1000000 + -1750x + x2 = 0 + 1000000 Combine like terms: -1000000 + 1000000 = 0 0 + -1750x + x2 = 0 + 1000000 -1750x + x2 = 0 + 1000000 Combine like terms: 0 + 1000000 = 1000000 -1750x + x2 = 1000000 The x term is -1750x. Take half its coefficient (-875). Square it (765625) and add it to both sides. Add '765625' to each side of the equation. -1750x + 765625 + x2 = 1000000 + 765625 Reorder the terms: 765625 + -1750x + x2 = 1000000 + 765625 Combine like terms: 1000000 + 765625 = 1765625 765625 + -1750x + x2 = 1765625 Factor a perfect square on the left side: (x + -875)(x + -875) = 1765625 Calculate the square root of the right side: 1328.768226592 Break this problem into two subproblems by setting (x + -875) equal to 1328.768226592 and -1328.768226592.Subproblem 1
x + -875 = 1328.768226592 Simplifying x + -875 = 1328.768226592 Reorder the terms: -875 + x = 1328.768226592 Solving -875 + x = 1328.768226592 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '875' to each side of the equation. -875 + 875 + x = 1328.768226592 + 875 Combine like terms: -875 + 875 = 0 0 + x = 1328.768226592 + 875 x = 1328.768226592 + 875 Combine like terms: 1328.768226592 + 875 = 2203.768226592 x = 2203.768226592 Simplifying x = 2203.768226592Subproblem 2
x + -875 = -1328.768226592 Simplifying x + -875 = -1328.768226592 Reorder the terms: -875 + x = -1328.768226592 Solving -875 + x = -1328.768226592 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '875' to each side of the equation. -875 + 875 + x = -1328.768226592 + 875 Combine like terms: -875 + 875 = 0 0 + x = -1328.768226592 + 875 x = -1328.768226592 + 875 Combine like terms: -1328.768226592 + 875 = -453.768226592 x = -453.768226592 Simplifying x = -453.768226592Solution
The solution to the problem is based on the solutions from the subproblems. x = {2203.768226592, -453.768226592}
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