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Simplifying 7x2 + -48x + 24 = 0 Reorder the terms: 24 + -48x + 7x2 = 0 Solving 24 + -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'. 3.428571429 + -6.857142857x + x2 = 0 Move the constant term to the right: Add '-3.428571429' to each side of the equation. 3.428571429 + -6.857142857x + -3.428571429 + x2 = 0 + -3.428571429 Reorder the terms: 3.428571429 + -3.428571429 + -6.857142857x + x2 = 0 + -3.428571429 Combine like terms: 3.428571429 + -3.428571429 = 0.000000000 0.000000000 + -6.857142857x + x2 = 0 + -3.428571429 -6.857142857x + x2 = 0 + -3.428571429 Combine like terms: 0 + -3.428571429 = -3.428571429 -6.857142857x + x2 = -3.428571429 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 = -3.428571429 + 11.75510204 Reorder the terms: 11.75510204 + -6.857142857x + x2 = -3.428571429 + 11.75510204 Combine like terms: -3.428571429 + 11.75510204 = 8.326530611 11.75510204 + -6.857142857x + x2 = 8.326530611 Factor a perfect square on the left side: (x + -3.428571429)(x + -3.428571429) = 8.326530611 Calculate the square root of the right side: 2.885572839 Break this problem into two subproblems by setting (x + -3.428571429) equal to 2.885572839 and -2.885572839.Subproblem 1
x + -3.428571429 = 2.885572839 Simplifying x + -3.428571429 = 2.885572839 Reorder the terms: -3.428571429 + x = 2.885572839 Solving -3.428571429 + x = 2.885572839 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 = 2.885572839 + 3.428571429 Combine like terms: -3.428571429 + 3.428571429 = 0.000000000 0.000000000 + x = 2.885572839 + 3.428571429 x = 2.885572839 + 3.428571429 Combine like terms: 2.885572839 + 3.428571429 = 6.314144268 x = 6.314144268 Simplifying x = 6.314144268Subproblem 2
x + -3.428571429 = -2.885572839 Simplifying x + -3.428571429 = -2.885572839 Reorder the terms: -3.428571429 + x = -2.885572839 Solving -3.428571429 + x = -2.885572839 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 = -2.885572839 + 3.428571429 Combine like terms: -3.428571429 + 3.428571429 = 0.000000000 0.000000000 + x = -2.885572839 + 3.428571429 x = -2.885572839 + 3.428571429 Combine like terms: -2.885572839 + 3.428571429 = 0.54299859 x = 0.54299859 Simplifying x = 0.54299859Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.314144268, 0.54299859}
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