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Simplifying 3x2 + -41x + 102 = 0 Reorder the terms: 102 + -41x + 3x2 = 0 Solving 102 + -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'. 34 + -13.66666667x + x2 = 0 Move the constant term to the right: Add '-34' to each side of the equation. 34 + -13.66666667x + -34 + x2 = 0 + -34 Reorder the terms: 34 + -34 + -13.66666667x + x2 = 0 + -34 Combine like terms: 34 + -34 = 0 0 + -13.66666667x + x2 = 0 + -34 -13.66666667x + x2 = 0 + -34 Combine like terms: 0 + -34 = -34 -13.66666667x + x2 = -34 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 = -34 + 46.69444447 Reorder the terms: 46.69444447 + -13.66666667x + x2 = -34 + 46.69444447 Combine like terms: -34 + 46.69444447 = 12.69444447 46.69444447 + -13.66666667x + x2 = 12.69444447 Factor a perfect square on the left side: (x + -6.833333335)(x + -6.833333335) = 12.69444447 Calculate the square root of the right side: 3.562926391 Break this problem into two subproblems by setting (x + -6.833333335) equal to 3.562926391 and -3.562926391.Subproblem 1
x + -6.833333335 = 3.562926391 Simplifying x + -6.833333335 = 3.562926391 Reorder the terms: -6.833333335 + x = 3.562926391 Solving -6.833333335 + x = 3.562926391 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 = 3.562926391 + 6.833333335 Combine like terms: -6.833333335 + 6.833333335 = 0.000000000 0.000000000 + x = 3.562926391 + 6.833333335 x = 3.562926391 + 6.833333335 Combine like terms: 3.562926391 + 6.833333335 = 10.396259726 x = 10.396259726 Simplifying x = 10.396259726Subproblem 2
x + -6.833333335 = -3.562926391 Simplifying x + -6.833333335 = -3.562926391 Reorder the terms: -6.833333335 + x = -3.562926391 Solving -6.833333335 + x = -3.562926391 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 = -3.562926391 + 6.833333335 Combine like terms: -6.833333335 + 6.833333335 = 0.000000000 0.000000000 + x = -3.562926391 + 6.833333335 x = -3.562926391 + 6.833333335 Combine like terms: -3.562926391 + 6.833333335 = 3.270406944 x = 3.270406944 Simplifying x = 3.270406944Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.396259726, 3.270406944}
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