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Simplifying ((3x2) + -41x + 82) = 0 Reorder the terms: (82 + -41x + (3x2)) = 0 Remove parenthesis around (82 + -41x + (3x2)) 82 + -41x + (3x2) = 0 Solving 82 + -41x + (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'. 27.33333333 + -13.66666667x + x2 = 0 Move the constant term to the right: Add '-27.33333333' to each side of the equation. 27.33333333 + -13.66666667x + -27.33333333 + x2 = 0 + -27.33333333 Reorder the terms: 27.33333333 + -27.33333333 + -13.66666667x + x2 = 0 + -27.33333333 Combine like terms: 27.33333333 + -27.33333333 = 0.00000000 0.00000000 + -13.66666667x + x2 = 0 + -27.33333333 -13.66666667x + x2 = 0 + -27.33333333 Combine like terms: 0 + -27.33333333 = -27.33333333 -13.66666667x + x2 = -27.33333333 The x term is -13.66666667x. Take half its coefficient (-6.833333335). Square it (46.69444447) and add it to both sides. Add '46.69444447' to each side of the equation. -13.66666667x + 46.69444447 + x2 = -27.33333333 + 46.69444447 Reorder the terms: 46.69444447 + -13.66666667x + x2 = -27.33333333 + 46.69444447 Combine like terms: -27.33333333 + 46.69444447 = 19.36111114 46.69444447 + -13.66666667x + x2 = 19.36111114 Factor a perfect square on the left side: ((x) + -6.833333335)((x) + -6.833333335) = 19.36111114 Calculate the square root of the right side: 4.400126264 Break this problem into two subproblems by setting ((x) + -6.833333335) equal to 4.400126264 and -4.400126264.Subproblem 1
(x) + -6.833333335 = 4.400126264 Simplifying (x) + -6.833333335 = 4.400126264 x + -6.833333335 = 4.400126264 Reorder the terms: -6.833333335 + x = 4.400126264 Solving -6.833333335 + x = 4.400126264 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.833333335' to each side of the equation. -6.833333335 + 6.833333335 + x = 4.400126264 + 6.833333335 Combine like terms: -6.833333335 + 6.833333335 = 0.000000000 0.000000000 + x = 4.400126264 + 6.833333335 x = 4.400126264 + 6.833333335 Combine like terms: 4.400126264 + 6.833333335 = 11.233459599 x = 11.233459599 Simplifying x = 11.233459599Subproblem 2
(x) + -6.833333335 = -4.400126264 Simplifying (x) + -6.833333335 = -4.400126264 x + -6.833333335 = -4.400126264 Reorder the terms: -6.833333335 + x = -4.400126264 Solving -6.833333335 + x = -4.400126264 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.833333335' to each side of the equation. -6.833333335 + 6.833333335 + x = -4.400126264 + 6.833333335 Combine like terms: -6.833333335 + 6.833333335 = 0.000000000 0.000000000 + x = -4.400126264 + 6.833333335 x = -4.400126264 + 6.833333335 Combine like terms: -4.400126264 + 6.833333335 = 2.433207071 x = 2.433207071 Simplifying x = 2.433207071Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.233459599, 2.433207071}
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