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Simplifying 100x + x2 = 5000 Solving 100x + x2 = 5000 Solving for variable 'x'. Reorder the terms: -5000 + 100x + x2 = 5000 + -5000 Combine like terms: 5000 + -5000 = 0 -5000 + 100x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '5000' to each side of the equation. -5000 + 100x + 5000 + x2 = 0 + 5000 Reorder the terms: -5000 + 5000 + 100x + x2 = 0 + 5000 Combine like terms: -5000 + 5000 = 0 0 + 100x + x2 = 0 + 5000 100x + x2 = 0 + 5000 Combine like terms: 0 + 5000 = 5000 100x + x2 = 5000 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 = 5000 + 2500 Reorder the terms: 2500 + 100x + x2 = 5000 + 2500 Combine like terms: 5000 + 2500 = 7500 2500 + 100x + x2 = 7500 Factor a perfect square on the left side: (x + 50)(x + 50) = 7500 Calculate the square root of the right side: 86.602540378 Break this problem into two subproblems by setting (x + 50) equal to 86.602540378 and -86.602540378.Subproblem 1
x + 50 = 86.602540378 Simplifying x + 50 = 86.602540378 Reorder the terms: 50 + x = 86.602540378 Solving 50 + x = 86.602540378 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 = 86.602540378 + -50 Combine like terms: 50 + -50 = 0 0 + x = 86.602540378 + -50 x = 86.602540378 + -50 Combine like terms: 86.602540378 + -50 = 36.602540378 x = 36.602540378 Simplifying x = 36.602540378Subproblem 2
x + 50 = -86.602540378 Simplifying x + 50 = -86.602540378 Reorder the terms: 50 + x = -86.602540378 Solving 50 + x = -86.602540378 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 = -86.602540378 + -50 Combine like terms: 50 + -50 = 0 0 + x = -86.602540378 + -50 x = -86.602540378 + -50 Combine like terms: -86.602540378 + -50 = -136.602540378 x = -136.602540378 Simplifying x = -136.602540378Solution
The solution to the problem is based on the solutions from the subproblems. x = {36.602540378, -136.602540378}
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