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Simplifying 0 = -1x2 + 202x + -5000 Reorder the terms: 0 = -5000 + 202x + -1x2 Solving 0 = -5000 + 202x + -1x2 Solving for variable 'x'. Combine like terms: 0 + 5000 = 5000 5000 + -202x + x2 = -5000 + 202x + -1x2 + 5000 + -202x + x2 Reorder the terms: 5000 + -202x + x2 = -5000 + 5000 + 202x + -202x + -1x2 + x2 Combine like terms: -5000 + 5000 = 0 5000 + -202x + x2 = 0 + 202x + -202x + -1x2 + x2 5000 + -202x + x2 = 202x + -202x + -1x2 + x2 Combine like terms: 202x + -202x = 0 5000 + -202x + x2 = 0 + -1x2 + x2 5000 + -202x + x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 5000 + -202x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-5000' to each side of the equation. 5000 + -202x + -5000 + x2 = 0 + -5000 Reorder the terms: 5000 + -5000 + -202x + x2 = 0 + -5000 Combine like terms: 5000 + -5000 = 0 0 + -202x + x2 = 0 + -5000 -202x + x2 = 0 + -5000 Combine like terms: 0 + -5000 = -5000 -202x + x2 = -5000 The x term is -202x. Take half its coefficient (-101). Square it (10201) and add it to both sides. Add '10201' to each side of the equation. -202x + 10201 + x2 = -5000 + 10201 Reorder the terms: 10201 + -202x + x2 = -5000 + 10201 Combine like terms: -5000 + 10201 = 5201 10201 + -202x + x2 = 5201 Factor a perfect square on the left side: (x + -101)(x + -101) = 5201 Calculate the square root of the right side: 72.117958928 Break this problem into two subproblems by setting (x + -101) equal to 72.117958928 and -72.117958928.Subproblem 1
x + -101 = 72.117958928 Simplifying x + -101 = 72.117958928 Reorder the terms: -101 + x = 72.117958928 Solving -101 + x = 72.117958928 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '101' to each side of the equation. -101 + 101 + x = 72.117958928 + 101 Combine like terms: -101 + 101 = 0 0 + x = 72.117958928 + 101 x = 72.117958928 + 101 Combine like terms: 72.117958928 + 101 = 173.117958928 x = 173.117958928 Simplifying x = 173.117958928Subproblem 2
x + -101 = -72.117958928 Simplifying x + -101 = -72.117958928 Reorder the terms: -101 + x = -72.117958928 Solving -101 + x = -72.117958928 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '101' to each side of the equation. -101 + 101 + x = -72.117958928 + 101 Combine like terms: -101 + 101 = 0 0 + x = -72.117958928 + 101 x = -72.117958928 + 101 Combine like terms: -72.117958928 + 101 = 28.882041072 x = 28.882041072 Simplifying x = 28.882041072Solution
The solution to the problem is based on the solutions from the subproblems. x = {173.117958928, 28.882041072}
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