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Simplifying 49x2 + -8862x + 48617 = 0 Reorder the terms: 48617 + -8862x + 49x2 = 0 Solving 48617 + -8862x + 49x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 49 the coefficient of the squared term: Divide each side by '49'. 992.1836735 + -180.8571429x + x2 = 0 Move the constant term to the right: Add '-992.1836735' to each side of the equation. 992.1836735 + -180.8571429x + -992.1836735 + x2 = 0 + -992.1836735 Reorder the terms: 992.1836735 + -992.1836735 + -180.8571429x + x2 = 0 + -992.1836735 Combine like terms: 992.1836735 + -992.1836735 = 0.0000000 0.0000000 + -180.8571429x + x2 = 0 + -992.1836735 -180.8571429x + x2 = 0 + -992.1836735 Combine like terms: 0 + -992.1836735 = -992.1836735 -180.8571429x + x2 = -992.1836735 The x term is -180.8571429x. Take half its coefficient (-90.42857145). Square it (8177.326534) and add it to both sides. Add '8177.326534' to each side of the equation. -180.8571429x + 8177.326534 + x2 = -992.1836735 + 8177.326534 Reorder the terms: 8177.326534 + -180.8571429x + x2 = -992.1836735 + 8177.326534 Combine like terms: -992.1836735 + 8177.326534 = 7185.1428605 8177.326534 + -180.8571429x + x2 = 7185.1428605 Factor a perfect square on the left side: (x + -90.42857145)(x + -90.42857145) = 7185.1428605 Calculate the square root of the right side: 84.765221999 Break this problem into two subproblems by setting (x + -90.42857145) equal to 84.765221999 and -84.765221999.Subproblem 1
x + -90.42857145 = 84.765221999 Simplifying x + -90.42857145 = 84.765221999 Reorder the terms: -90.42857145 + x = 84.765221999 Solving -90.42857145 + x = 84.765221999 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '90.42857145' to each side of the equation. -90.42857145 + 90.42857145 + x = 84.765221999 + 90.42857145 Combine like terms: -90.42857145 + 90.42857145 = 0.00000000 0.00000000 + x = 84.765221999 + 90.42857145 x = 84.765221999 + 90.42857145 Combine like terms: 84.765221999 + 90.42857145 = 175.193793449 x = 175.193793449 Simplifying x = 175.193793449Subproblem 2
x + -90.42857145 = -84.765221999 Simplifying x + -90.42857145 = -84.765221999 Reorder the terms: -90.42857145 + x = -84.765221999 Solving -90.42857145 + x = -84.765221999 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '90.42857145' to each side of the equation. -90.42857145 + 90.42857145 + x = -84.765221999 + 90.42857145 Combine like terms: -90.42857145 + 90.42857145 = 0.00000000 0.00000000 + x = -84.765221999 + 90.42857145 x = -84.765221999 + 90.42857145 Combine like terms: -84.765221999 + 90.42857145 = 5.663349451 x = 5.663349451 Simplifying x = 5.663349451Solution
The solution to the problem is based on the solutions from the subproblems. x = {175.193793449, 5.663349451}
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