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Simplifying 7x2 + -48x + -46 = 0 Reorder the terms: -46 + -48x + 7x2 = 0 Solving -46 + -48x + 7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -6.571428571 + -6.857142857x + x2 = 0 Move the constant term to the right: Add '6.571428571' to each side of the equation. -6.571428571 + -6.857142857x + 6.571428571 + x2 = 0 + 6.571428571 Reorder the terms: -6.571428571 + 6.571428571 + -6.857142857x + x2 = 0 + 6.571428571 Combine like terms: -6.571428571 + 6.571428571 = 0.000000000 0.000000000 + -6.857142857x + x2 = 0 + 6.571428571 -6.857142857x + x2 = 0 + 6.571428571 Combine like terms: 0 + 6.571428571 = 6.571428571 -6.857142857x + x2 = 6.571428571 The x term is -6.857142857x. Take half its coefficient (-3.428571429). Square it (11.75510204) and add it to both sides. Add '11.75510204' to each side of the equation. -6.857142857x + 11.75510204 + x2 = 6.571428571 + 11.75510204 Reorder the terms: 11.75510204 + -6.857142857x + x2 = 6.571428571 + 11.75510204 Combine like terms: 6.571428571 + 11.75510204 = 18.326530611 11.75510204 + -6.857142857x + x2 = 18.326530611 Factor a perfect square on the left side: (x + -3.428571429)(x + -3.428571429) = 18.326530611 Calculate the square root of the right side: 4.280949732 Break this problem into two subproblems by setting (x + -3.428571429) equal to 4.280949732 and -4.280949732.Subproblem 1
x + -3.428571429 = 4.280949732 Simplifying x + -3.428571429 = 4.280949732 Reorder the terms: -3.428571429 + x = 4.280949732 Solving -3.428571429 + x = 4.280949732 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.428571429' to each side of the equation. -3.428571429 + 3.428571429 + x = 4.280949732 + 3.428571429 Combine like terms: -3.428571429 + 3.428571429 = 0.000000000 0.000000000 + x = 4.280949732 + 3.428571429 x = 4.280949732 + 3.428571429 Combine like terms: 4.280949732 + 3.428571429 = 7.709521161 x = 7.709521161 Simplifying x = 7.709521161Subproblem 2
x + -3.428571429 = -4.280949732 Simplifying x + -3.428571429 = -4.280949732 Reorder the terms: -3.428571429 + x = -4.280949732 Solving -3.428571429 + x = -4.280949732 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.428571429' to each side of the equation. -3.428571429 + 3.428571429 + x = -4.280949732 + 3.428571429 Combine like terms: -3.428571429 + 3.428571429 = 0.000000000 0.000000000 + x = -4.280949732 + 3.428571429 x = -4.280949732 + 3.428571429 Combine like terms: -4.280949732 + 3.428571429 = -0.852378303 x = -0.852378303 Simplifying x = -0.852378303Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.709521161, -0.852378303}
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