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Simplifying 7x2 + -48x + -34 = 0 Reorder the terms: -34 + -48x + 7x2 = 0 Solving -34 + -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'. -4.857142857 + -6.857142857x + x2 = 0 Move the constant term to the right: Add '4.857142857' to each side of the equation. -4.857142857 + -6.857142857x + 4.857142857 + x2 = 0 + 4.857142857 Reorder the terms: -4.857142857 + 4.857142857 + -6.857142857x + x2 = 0 + 4.857142857 Combine like terms: -4.857142857 + 4.857142857 = 0.000000000 0.000000000 + -6.857142857x + x2 = 0 + 4.857142857 -6.857142857x + x2 = 0 + 4.857142857 Combine like terms: 0 + 4.857142857 = 4.857142857 -6.857142857x + x2 = 4.857142857 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 = 4.857142857 + 11.75510204 Reorder the terms: 11.75510204 + -6.857142857x + x2 = 4.857142857 + 11.75510204 Combine like terms: 4.857142857 + 11.75510204 = 16.612244897 11.75510204 + -6.857142857x + x2 = 16.612244897 Factor a perfect square on the left side: (x + -3.428571429)(x + -3.428571429) = 16.612244897 Calculate the square root of the right side: 4.075812176 Break this problem into two subproblems by setting (x + -3.428571429) equal to 4.075812176 and -4.075812176.Subproblem 1
x + -3.428571429 = 4.075812176 Simplifying x + -3.428571429 = 4.075812176 Reorder the terms: -3.428571429 + x = 4.075812176 Solving -3.428571429 + x = 4.075812176 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 = 4.075812176 + 3.428571429 Combine like terms: -3.428571429 + 3.428571429 = 0.000000000 0.000000000 + x = 4.075812176 + 3.428571429 x = 4.075812176 + 3.428571429 Combine like terms: 4.075812176 + 3.428571429 = 7.504383605 x = 7.504383605 Simplifying x = 7.504383605Subproblem 2
x + -3.428571429 = -4.075812176 Simplifying x + -3.428571429 = -4.075812176 Reorder the terms: -3.428571429 + x = -4.075812176 Solving -3.428571429 + x = -4.075812176 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 = -4.075812176 + 3.428571429 Combine like terms: -3.428571429 + 3.428571429 = 0.000000000 0.000000000 + x = -4.075812176 + 3.428571429 x = -4.075812176 + 3.428571429 Combine like terms: -4.075812176 + 3.428571429 = -0.647240747 x = -0.647240747 Simplifying x = -0.647240747Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.504383605, -0.647240747}
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