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Simplifying -100x + 3000 = 60 + x * x Reorder the terms: 3000 + -100x = 60 + x * x Multiply x * x 3000 + -100x = 60 + x2 Solving 3000 + -100x = 60 + x2 Solving for variable 'x'. Reorder the terms: 3000 + -60 + -100x + -1x2 = 60 + x2 + -60 + -1x2 Combine like terms: 3000 + -60 = 2940 2940 + -100x + -1x2 = 60 + x2 + -60 + -1x2 Reorder the terms: 2940 + -100x + -1x2 = 60 + -60 + x2 + -1x2 Combine like terms: 60 + -60 = 0 2940 + -100x + -1x2 = 0 + x2 + -1x2 2940 + -100x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 2940 + -100x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -2940 + 100x + x2 = 0 Move the constant term to the right: Add '2940' to each side of the equation. -2940 + 100x + 2940 + x2 = 0 + 2940 Reorder the terms: -2940 + 2940 + 100x + x2 = 0 + 2940 Combine like terms: -2940 + 2940 = 0 0 + 100x + x2 = 0 + 2940 100x + x2 = 0 + 2940 Combine like terms: 0 + 2940 = 2940 100x + x2 = 2940 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 = 2940 + 2500 Reorder the terms: 2500 + 100x + x2 = 2940 + 2500 Combine like terms: 2940 + 2500 = 5440 2500 + 100x + x2 = 5440 Factor a perfect square on the left side: (x + 50)(x + 50) = 5440 Calculate the square root of the right side: 73.756355658 Break this problem into two subproblems by setting (x + 50) equal to 73.756355658 and -73.756355658.Subproblem 1
x + 50 = 73.756355658 Simplifying x + 50 = 73.756355658 Reorder the terms: 50 + x = 73.756355658 Solving 50 + x = 73.756355658 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 = 73.756355658 + -50 Combine like terms: 50 + -50 = 0 0 + x = 73.756355658 + -50 x = 73.756355658 + -50 Combine like terms: 73.756355658 + -50 = 23.756355658 x = 23.756355658 Simplifying x = 23.756355658Subproblem 2
x + 50 = -73.756355658 Simplifying x + 50 = -73.756355658 Reorder the terms: 50 + x = -73.756355658 Solving 50 + x = -73.756355658 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 = -73.756355658 + -50 Combine like terms: 50 + -50 = 0 0 + x = -73.756355658 + -50 x = -73.756355658 + -50 Combine like terms: -73.756355658 + -50 = -123.756355658 x = -123.756355658 Simplifying x = -123.756355658Solution
The solution to the problem is based on the solutions from the subproblems. x = {23.756355658, -123.756355658}
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