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Simplifying 7x2 + -48x + 34 = 2 Reorder the terms: 34 + -48x + 7x2 = 2 Solving 34 + -48x + 7x2 = 2 Solving for variable 'x'. Reorder the terms: 34 + -2 + -48x + 7x2 = 2 + -2 Combine like terms: 34 + -2 = 32 32 + -48x + 7x2 = 2 + -2 Combine like terms: 2 + -2 = 0 32 + -48x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 4.571428571 + -6.857142857x + x2 = 0 Move the constant term to the right: Add '-4.571428571' to each side of the equation. 4.571428571 + -6.857142857x + -4.571428571 + x2 = 0 + -4.571428571 Reorder the terms: 4.571428571 + -4.571428571 + -6.857142857x + x2 = 0 + -4.571428571 Combine like terms: 4.571428571 + -4.571428571 = 0.000000000 0.000000000 + -6.857142857x + x2 = 0 + -4.571428571 -6.857142857x + x2 = 0 + -4.571428571 Combine like terms: 0 + -4.571428571 = -4.571428571 -6.857142857x + x2 = -4.571428571 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 = -4.571428571 + 11.75510204 Reorder the terms: 11.75510204 + -6.857142857x + x2 = -4.571428571 + 11.75510204 Combine like terms: -4.571428571 + 11.75510204 = 7.183673469 11.75510204 + -6.857142857x + x2 = 7.183673469 Factor a perfect square on the left side: (x + -3.428571429)(x + -3.428571429) = 7.183673469 Calculate the square root of the right side: 2.680237577 Break this problem into two subproblems by setting (x + -3.428571429) equal to 2.680237577 and -2.680237577.Subproblem 1
x + -3.428571429 = 2.680237577 Simplifying x + -3.428571429 = 2.680237577 Reorder the terms: -3.428571429 + x = 2.680237577 Solving -3.428571429 + x = 2.680237577 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 = 2.680237577 + 3.428571429 Combine like terms: -3.428571429 + 3.428571429 = 0.000000000 0.000000000 + x = 2.680237577 + 3.428571429 x = 2.680237577 + 3.428571429 Combine like terms: 2.680237577 + 3.428571429 = 6.108809006 x = 6.108809006 Simplifying x = 6.108809006Subproblem 2
x + -3.428571429 = -2.680237577 Simplifying x + -3.428571429 = -2.680237577 Reorder the terms: -3.428571429 + x = -2.680237577 Solving -3.428571429 + x = -2.680237577 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 = -2.680237577 + 3.428571429 Combine like terms: -3.428571429 + 3.428571429 = 0.000000000 0.000000000 + x = -2.680237577 + 3.428571429 x = -2.680237577 + 3.428571429 Combine like terms: -2.680237577 + 3.428571429 = 0.748333852 x = 0.748333852 Simplifying x = 0.748333852Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.108809006, 0.748333852}
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