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Simplifying 100x = 1440000 + -1x2 Solving 100x = 1440000 + -1x2 Solving for variable 'x'. Reorder the terms: -1440000 + 100x + x2 = 1440000 + -1x2 + -1440000 + x2 Reorder the terms: -1440000 + 100x + x2 = 1440000 + -1440000 + -1x2 + x2 Combine like terms: 1440000 + -1440000 = 0 -1440000 + 100x + x2 = 0 + -1x2 + x2 -1440000 + 100x + x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 -1440000 + 100x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '1440000' to each side of the equation. -1440000 + 100x + 1440000 + x2 = 0 + 1440000 Reorder the terms: -1440000 + 1440000 + 100x + x2 = 0 + 1440000 Combine like terms: -1440000 + 1440000 = 0 0 + 100x + x2 = 0 + 1440000 100x + x2 = 0 + 1440000 Combine like terms: 0 + 1440000 = 1440000 100x + x2 = 1440000 The x term is 100x. Take half its coefficient (50). Square it (2500) and add it to both sides. Add '2500' to each side of the equation. 100x + 2500 + x2 = 1440000 + 2500 Reorder the terms: 2500 + 100x + x2 = 1440000 + 2500 Combine like terms: 1440000 + 2500 = 1442500 2500 + 100x + x2 = 1442500 Factor a perfect square on the left side: (x + 50)(x + 50) = 1442500 Calculate the square root of the right side: 1201.041214946 Break this problem into two subproblems by setting (x + 50) equal to 1201.041214946 and -1201.041214946.Subproblem 1
x + 50 = 1201.041214946 Simplifying x + 50 = 1201.041214946 Reorder the terms: 50 + x = 1201.041214946 Solving 50 + x = 1201.041214946 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-50' to each side of the equation. 50 + -50 + x = 1201.041214946 + -50 Combine like terms: 50 + -50 = 0 0 + x = 1201.041214946 + -50 x = 1201.041214946 + -50 Combine like terms: 1201.041214946 + -50 = 1151.041214946 x = 1151.041214946 Simplifying x = 1151.041214946Subproblem 2
x + 50 = -1201.041214946 Simplifying x + 50 = -1201.041214946 Reorder the terms: 50 + x = -1201.041214946 Solving 50 + x = -1201.041214946 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-50' to each side of the equation. 50 + -50 + x = -1201.041214946 + -50 Combine like terms: 50 + -50 = 0 0 + x = -1201.041214946 + -50 x = -1201.041214946 + -50 Combine like terms: -1201.041214946 + -50 = -1251.041214946 x = -1251.041214946 Simplifying x = -1251.041214946Solution
The solution to the problem is based on the solutions from the subproblems. x = {1151.041214946, -1251.041214946}
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