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Simplifying -2340x2 + 34368x + -118675 = 0 Reorder the terms: -118675 + 34368x + -2340x2 = 0 Solving -118675 + 34368x + -2340x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -2340 the coefficient of the squared term: Divide each side by '-2340'. 50.71581197 + -14.68717949x + x2 = 0 Move the constant term to the right: Add '-50.71581197' to each side of the equation. 50.71581197 + -14.68717949x + -50.71581197 + x2 = 0 + -50.71581197 Reorder the terms: 50.71581197 + -50.71581197 + -14.68717949x + x2 = 0 + -50.71581197 Combine like terms: 50.71581197 + -50.71581197 = 0.00000000 0.00000000 + -14.68717949x + x2 = 0 + -50.71581197 -14.68717949x + x2 = 0 + -50.71581197 Combine like terms: 0 + -50.71581197 = -50.71581197 -14.68717949x + x2 = -50.71581197 The x term is -14.68717949x. Take half its coefficient (-7.343589745). Square it (53.92831034) and add it to both sides. Add '53.92831034' to each side of the equation. -14.68717949x + 53.92831034 + x2 = -50.71581197 + 53.92831034 Reorder the terms: 53.92831034 + -14.68717949x + x2 = -50.71581197 + 53.92831034 Combine like terms: -50.71581197 + 53.92831034 = 3.21249837 53.92831034 + -14.68717949x + x2 = 3.21249837 Factor a perfect square on the left side: (x + -7.343589745)(x + -7.343589745) = 3.21249837 Calculate the square root of the right side: 1.792344378 Break this problem into two subproblems by setting (x + -7.343589745) equal to 1.792344378 and -1.792344378.Subproblem 1
x + -7.343589745 = 1.792344378 Simplifying x + -7.343589745 = 1.792344378 Reorder the terms: -7.343589745 + x = 1.792344378 Solving -7.343589745 + x = 1.792344378 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.343589745' to each side of the equation. -7.343589745 + 7.343589745 + x = 1.792344378 + 7.343589745 Combine like terms: -7.343589745 + 7.343589745 = 0.000000000 0.000000000 + x = 1.792344378 + 7.343589745 x = 1.792344378 + 7.343589745 Combine like terms: 1.792344378 + 7.343589745 = 9.135934123 x = 9.135934123 Simplifying x = 9.135934123Subproblem 2
x + -7.343589745 = -1.792344378 Simplifying x + -7.343589745 = -1.792344378 Reorder the terms: -7.343589745 + x = -1.792344378 Solving -7.343589745 + x = -1.792344378 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.343589745' to each side of the equation. -7.343589745 + 7.343589745 + x = -1.792344378 + 7.343589745 Combine like terms: -7.343589745 + 7.343589745 = 0.000000000 0.000000000 + x = -1.792344378 + 7.343589745 x = -1.792344378 + 7.343589745 Combine like terms: -1.792344378 + 7.343589745 = 5.551245367 x = 5.551245367 Simplifying x = 5.551245367Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.135934123, 5.551245367}
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