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Simplifying 3x2 + -41x = -10 Reorder the terms: -41x + 3x2 = -10 Solving -41x + 3x2 = -10 Solving for variable 'x'. Reorder the terms: 10 + -41x + 3x2 = -10 + 10 Combine like terms: -10 + 10 = 0 10 + -41x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 3.333333333 + -13.66666667x + x2 = 0 Move the constant term to the right: Add '-3.333333333' to each side of the equation. 3.333333333 + -13.66666667x + -3.333333333 + x2 = 0 + -3.333333333 Reorder the terms: 3.333333333 + -3.333333333 + -13.66666667x + x2 = 0 + -3.333333333 Combine like terms: 3.333333333 + -3.333333333 = 0.000000000 0.000000000 + -13.66666667x + x2 = 0 + -3.333333333 -13.66666667x + x2 = 0 + -3.333333333 Combine like terms: 0 + -3.333333333 = -3.333333333 -13.66666667x + x2 = -3.333333333 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 = -3.333333333 + 46.69444447 Reorder the terms: 46.69444447 + -13.66666667x + x2 = -3.333333333 + 46.69444447 Combine like terms: -3.333333333 + 46.69444447 = 43.361111137 46.69444447 + -13.66666667x + x2 = 43.361111137 Factor a perfect square on the left side: (x + -6.833333335)(x + -6.833333335) = 43.361111137 Calculate the square root of the right side: 6.584915424 Break this problem into two subproblems by setting (x + -6.833333335) equal to 6.584915424 and -6.584915424.Subproblem 1
x + -6.833333335 = 6.584915424 Simplifying x + -6.833333335 = 6.584915424 Reorder the terms: -6.833333335 + x = 6.584915424 Solving -6.833333335 + x = 6.584915424 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 = 6.584915424 + 6.833333335 Combine like terms: -6.833333335 + 6.833333335 = 0.000000000 0.000000000 + x = 6.584915424 + 6.833333335 x = 6.584915424 + 6.833333335 Combine like terms: 6.584915424 + 6.833333335 = 13.418248759 x = 13.418248759 Simplifying x = 13.418248759Subproblem 2
x + -6.833333335 = -6.584915424 Simplifying x + -6.833333335 = -6.584915424 Reorder the terms: -6.833333335 + x = -6.584915424 Solving -6.833333335 + x = -6.584915424 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 = -6.584915424 + 6.833333335 Combine like terms: -6.833333335 + 6.833333335 = 0.000000000 0.000000000 + x = -6.584915424 + 6.833333335 x = -6.584915424 + 6.833333335 Combine like terms: -6.584915424 + 6.833333335 = 0.248417911 x = 0.248417911 Simplifying x = 0.248417911Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.418248759, 0.248417911}
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