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Simplifying 3x2 + -41x + 105 = 0 Reorder the terms: 105 + -41x + 3x2 = 0 Solving 105 + -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'. 35 + -13.66666667x + x2 = 0 Move the constant term to the right: Add '-35' to each side of the equation. 35 + -13.66666667x + -35 + x2 = 0 + -35 Reorder the terms: 35 + -35 + -13.66666667x + x2 = 0 + -35 Combine like terms: 35 + -35 = 0 0 + -13.66666667x + x2 = 0 + -35 -13.66666667x + x2 = 0 + -35 Combine like terms: 0 + -35 = -35 -13.66666667x + x2 = -35 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 = -35 + 46.69444447 Reorder the terms: 46.69444447 + -13.66666667x + x2 = -35 + 46.69444447 Combine like terms: -35 + 46.69444447 = 11.69444447 46.69444447 + -13.66666667x + x2 = 11.69444447 Factor a perfect square on the left side: (x + -6.833333335)(x + -6.833333335) = 11.69444447 Calculate the square root of the right side: 3.419714092 Break this problem into two subproblems by setting (x + -6.833333335) equal to 3.419714092 and -3.419714092.Subproblem 1
x + -6.833333335 = 3.419714092 Simplifying x + -6.833333335 = 3.419714092 Reorder the terms: -6.833333335 + x = 3.419714092 Solving -6.833333335 + x = 3.419714092 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 = 3.419714092 + 6.833333335 Combine like terms: -6.833333335 + 6.833333335 = 0.000000000 0.000000000 + x = 3.419714092 + 6.833333335 x = 3.419714092 + 6.833333335 Combine like terms: 3.419714092 + 6.833333335 = 10.253047427 x = 10.253047427 Simplifying x = 10.253047427Subproblem 2
x + -6.833333335 = -3.419714092 Simplifying x + -6.833333335 = -3.419714092 Reorder the terms: -6.833333335 + x = -3.419714092 Solving -6.833333335 + x = -3.419714092 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 = -3.419714092 + 6.833333335 Combine like terms: -6.833333335 + 6.833333335 = 0.000000000 0.000000000 + x = -3.419714092 + 6.833333335 x = -3.419714092 + 6.833333335 Combine like terms: -3.419714092 + 6.833333335 = 3.413619243 x = 3.413619243 Simplifying x = 3.413619243Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.253047427, 3.413619243}
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