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Simplifying 3x2 + -43x + 120 = 0 Reorder the terms: 120 + -43x + 3x2 = 0 Solving 120 + -43x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 40 + -14.33333333x + x2 = 0 Move the constant term to the right: Add '-40' to each side of the equation. 40 + -14.33333333x + -40 + x2 = 0 + -40 Reorder the terms: 40 + -40 + -14.33333333x + x2 = 0 + -40 Combine like terms: 40 + -40 = 0 0 + -14.33333333x + x2 = 0 + -40 -14.33333333x + x2 = 0 + -40 Combine like terms: 0 + -40 = -40 -14.33333333x + x2 = -40 The x term is -14.33333333x. Take half its coefficient (-7.166666665). Square it (51.36111109) and add it to both sides. Add '51.36111109' to each side of the equation. -14.33333333x + 51.36111109 + x2 = -40 + 51.36111109 Reorder the terms: 51.36111109 + -14.33333333x + x2 = -40 + 51.36111109 Combine like terms: -40 + 51.36111109 = 11.36111109 51.36111109 + -14.33333333x + x2 = 11.36111109 Factor a perfect square on the left side: (x + -7.166666665)(x + -7.166666665) = 11.36111109 Calculate the square root of the right side: 3.370624733 Break this problem into two subproblems by setting (x + -7.166666665) equal to 3.370624733 and -3.370624733.Subproblem 1
x + -7.166666665 = 3.370624733 Simplifying x + -7.166666665 = 3.370624733 Reorder the terms: -7.166666665 + x = 3.370624733 Solving -7.166666665 + x = 3.370624733 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.166666665' to each side of the equation. -7.166666665 + 7.166666665 + x = 3.370624733 + 7.166666665 Combine like terms: -7.166666665 + 7.166666665 = 0.000000000 0.000000000 + x = 3.370624733 + 7.166666665 x = 3.370624733 + 7.166666665 Combine like terms: 3.370624733 + 7.166666665 = 10.537291398 x = 10.537291398 Simplifying x = 10.537291398Subproblem 2
x + -7.166666665 = -3.370624733 Simplifying x + -7.166666665 = -3.370624733 Reorder the terms: -7.166666665 + x = -3.370624733 Solving -7.166666665 + x = -3.370624733 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.166666665' to each side of the equation. -7.166666665 + 7.166666665 + x = -3.370624733 + 7.166666665 Combine like terms: -7.166666665 + 7.166666665 = 0.000000000 0.000000000 + x = -3.370624733 + 7.166666665 x = -3.370624733 + 7.166666665 Combine like terms: -3.370624733 + 7.166666665 = 3.796041932 x = 3.796041932 Simplifying x = 3.796041932Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.537291398, 3.796041932}
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