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Simplifying -50x + 3000 = 60 + x * x Reorder the terms: 3000 + -50x = 60 + x * x Multiply x * x 3000 + -50x = 60 + x2 Solving 3000 + -50x = 60 + x2 Solving for variable 'x'. Reorder the terms: 3000 + -60 + -50x + -1x2 = 60 + x2 + -60 + -1x2 Combine like terms: 3000 + -60 = 2940 2940 + -50x + -1x2 = 60 + x2 + -60 + -1x2 Reorder the terms: 2940 + -50x + -1x2 = 60 + -60 + x2 + -1x2 Combine like terms: 60 + -60 = 0 2940 + -50x + -1x2 = 0 + x2 + -1x2 2940 + -50x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 2940 + -50x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -2940 + 50x + x2 = 0 Move the constant term to the right: Add '2940' to each side of the equation. -2940 + 50x + 2940 + x2 = 0 + 2940 Reorder the terms: -2940 + 2940 + 50x + x2 = 0 + 2940 Combine like terms: -2940 + 2940 = 0 0 + 50x + x2 = 0 + 2940 50x + x2 = 0 + 2940 Combine like terms: 0 + 2940 = 2940 50x + x2 = 2940 The x term is 50x. Take half its coefficient (25). Square it (625) and add it to both sides. Add '625' to each side of the equation. 50x + 625 + x2 = 2940 + 625 Reorder the terms: 625 + 50x + x2 = 2940 + 625 Combine like terms: 2940 + 625 = 3565 625 + 50x + x2 = 3565 Factor a perfect square on the left side: (x + 25)(x + 25) = 3565 Calculate the square root of the right side: 59.707620954 Break this problem into two subproblems by setting (x + 25) equal to 59.707620954 and -59.707620954.Subproblem 1
x + 25 = 59.707620954 Simplifying x + 25 = 59.707620954 Reorder the terms: 25 + x = 59.707620954 Solving 25 + x = 59.707620954 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-25' to each side of the equation. 25 + -25 + x = 59.707620954 + -25 Combine like terms: 25 + -25 = 0 0 + x = 59.707620954 + -25 x = 59.707620954 + -25 Combine like terms: 59.707620954 + -25 = 34.707620954 x = 34.707620954 Simplifying x = 34.707620954Subproblem 2
x + 25 = -59.707620954 Simplifying x + 25 = -59.707620954 Reorder the terms: 25 + x = -59.707620954 Solving 25 + x = -59.707620954 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-25' to each side of the equation. 25 + -25 + x = -59.707620954 + -25 Combine like terms: 25 + -25 = 0 0 + x = -59.707620954 + -25 x = -59.707620954 + -25 Combine like terms: -59.707620954 + -25 = -84.707620954 x = -84.707620954 Simplifying x = -84.707620954Solution
The solution to the problem is based on the solutions from the subproblems. x = {34.707620954, -84.707620954}
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