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Simplifying x2 + -2x + -200 = 5000 Reorder the terms: -200 + -2x + x2 = 5000 Solving -200 + -2x + x2 = 5000 Solving for variable 'x'. Reorder the terms: -200 + -5000 + -2x + x2 = 5000 + -5000 Combine like terms: -200 + -5000 = -5200 -5200 + -2x + x2 = 5000 + -5000 Combine like terms: 5000 + -5000 = 0 -5200 + -2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '5200' to each side of the equation. -5200 + -2x + 5200 + x2 = 0 + 5200 Reorder the terms: -5200 + 5200 + -2x + x2 = 0 + 5200 Combine like terms: -5200 + 5200 = 0 0 + -2x + x2 = 0 + 5200 -2x + x2 = 0 + 5200 Combine like terms: 0 + 5200 = 5200 -2x + x2 = 5200 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 5200 + 1 Reorder the terms: 1 + -2x + x2 = 5200 + 1 Combine like terms: 5200 + 1 = 5201 1 + -2x + x2 = 5201 Factor a perfect square on the left side: (x + -1)(x + -1) = 5201 Calculate the square root of the right side: 72.117958928 Break this problem into two subproblems by setting (x + -1) equal to 72.117958928 and -72.117958928.Subproblem 1
x + -1 = 72.117958928 Simplifying x + -1 = 72.117958928 Reorder the terms: -1 + x = 72.117958928 Solving -1 + x = 72.117958928 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 72.117958928 + 1 Combine like terms: -1 + 1 = 0 0 + x = 72.117958928 + 1 x = 72.117958928 + 1 Combine like terms: 72.117958928 + 1 = 73.117958928 x = 73.117958928 Simplifying x = 73.117958928Subproblem 2
x + -1 = -72.117958928 Simplifying x + -1 = -72.117958928 Reorder the terms: -1 + x = -72.117958928 Solving -1 + x = -72.117958928 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -72.117958928 + 1 Combine like terms: -1 + 1 = 0 0 + x = -72.117958928 + 1 x = -72.117958928 + 1 Combine like terms: -72.117958928 + 1 = -71.117958928 x = -71.117958928 Simplifying x = -71.117958928Solution
The solution to the problem is based on the solutions from the subproblems. x = {73.117958928, -71.117958928}
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