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Simplifying (3x2) + -1(31x) + 60 = 0 Remove parenthesis around (31x) (3x2) + -1 * 31x + 60 = 0 Multiply -1 * 31 (3x2) + -31x + 60 = 0 Reorder the terms: 60 + -31x + (3x2) = 0 Solving 60 + -31x + (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'. 20 + -10.33333333x + x2 = 0 Move the constant term to the right: Add '-20' to each side of the equation. 20 + -10.33333333x + -20 + x2 = 0 + -20 Reorder the terms: 20 + -20 + -10.33333333x + x2 = 0 + -20 Combine like terms: 20 + -20 = 0 0 + -10.33333333x + x2 = 0 + -20 -10.33333333x + x2 = 0 + -20 Combine like terms: 0 + -20 = -20 -10.33333333x + x2 = -20 The x term is -10.33333333x. Take half its coefficient (-5.166666665). Square it (26.69444443) and add it to both sides. Add '26.69444443' to each side of the equation. -10.33333333x + 26.69444443 + x2 = -20 + 26.69444443 Reorder the terms: 26.69444443 + -10.33333333x + x2 = -20 + 26.69444443 Combine like terms: -20 + 26.69444443 = 6.69444443 26.69444443 + -10.33333333x + x2 = 6.69444443 Factor a perfect square on the left side: ((x) + -5.166666665)((x) + -5.166666665) = 6.69444443 Calculate the square root of the right side: 2.587362447 Break this problem into two subproblems by setting ((x) + -5.166666665) equal to 2.587362447 and -2.587362447.Subproblem 1
(x) + -5.166666665 = 2.587362447 Simplifying (x) + -5.166666665 = 2.587362447 x + -5.166666665 = 2.587362447 Reorder the terms: -5.166666665 + x = 2.587362447 Solving -5.166666665 + x = 2.587362447 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.166666665' to each side of the equation. -5.166666665 + 5.166666665 + x = 2.587362447 + 5.166666665 Combine like terms: -5.166666665 + 5.166666665 = 0.000000000 0.000000000 + x = 2.587362447 + 5.166666665 x = 2.587362447 + 5.166666665 Combine like terms: 2.587362447 + 5.166666665 = 7.754029112 x = 7.754029112 Simplifying x = 7.754029112Subproblem 2
(x) + -5.166666665 = -2.587362447 Simplifying (x) + -5.166666665 = -2.587362447 x + -5.166666665 = -2.587362447 Reorder the terms: -5.166666665 + x = -2.587362447 Solving -5.166666665 + x = -2.587362447 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.166666665' to each side of the equation. -5.166666665 + 5.166666665 + x = -2.587362447 + 5.166666665 Combine like terms: -5.166666665 + 5.166666665 = 0.000000000 0.000000000 + x = -2.587362447 + 5.166666665 x = -2.587362447 + 5.166666665 Combine like terms: -2.587362447 + 5.166666665 = 2.579304218 x = 2.579304218 Simplifying x = 2.579304218Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.754029112, 2.579304218}
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