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Simplifying 4.09x2 + -10.82x + 4.01 = 0 Reorder the terms: 4.01 + -10.82x + 4.09x2 = 0 Solving 4.01 + -10.82x + 4.09x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4.09 the coefficient of the squared term: Divide each side by '4.09'. 0.9804400978 + -2.645476773x + x2 = 0 Move the constant term to the right: Add '-0.9804400978' to each side of the equation. 0.9804400978 + -2.645476773x + -0.9804400978 + x2 = 0 + -0.9804400978 Reorder the terms: 0.9804400978 + -0.9804400978 + -2.645476773x + x2 = 0 + -0.9804400978 Combine like terms: 0.9804400978 + -0.9804400978 = 0.0000000000 0.0000000000 + -2.645476773x + x2 = 0 + -0.9804400978 -2.645476773x + x2 = 0 + -0.9804400978 Combine like terms: 0 + -0.9804400978 = -0.9804400978 -2.645476773x + x2 = -0.9804400978 The x term is -2.645476773x. Take half its coefficient (-1.322738387). Square it (1.749636840) and add it to both sides. Add '1.749636840' to each side of the equation. -2.645476773x + 1.749636840 + x2 = -0.9804400978 + 1.749636840 Reorder the terms: 1.749636840 + -2.645476773x + x2 = -0.9804400978 + 1.749636840 Combine like terms: -0.9804400978 + 1.749636840 = 0.7691967422 1.749636840 + -2.645476773x + x2 = 0.7691967422 Factor a perfect square on the left side: (x + -1.322738387)(x + -1.322738387) = 0.7691967422 Calculate the square root of the right side: 0.877038621 Break this problem into two subproblems by setting (x + -1.322738387) equal to 0.877038621 and -0.877038621.Subproblem 1
x + -1.322738387 = 0.877038621 Simplifying x + -1.322738387 = 0.877038621 Reorder the terms: -1.322738387 + x = 0.877038621 Solving -1.322738387 + x = 0.877038621 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.322738387' to each side of the equation. -1.322738387 + 1.322738387 + x = 0.877038621 + 1.322738387 Combine like terms: -1.322738387 + 1.322738387 = 0.000000000 0.000000000 + x = 0.877038621 + 1.322738387 x = 0.877038621 + 1.322738387 Combine like terms: 0.877038621 + 1.322738387 = 2.199777008 x = 2.199777008 Simplifying x = 2.199777008Subproblem 2
x + -1.322738387 = -0.877038621 Simplifying x + -1.322738387 = -0.877038621 Reorder the terms: -1.322738387 + x = -0.877038621 Solving -1.322738387 + x = -0.877038621 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.322738387' to each side of the equation. -1.322738387 + 1.322738387 + x = -0.877038621 + 1.322738387 Combine like terms: -1.322738387 + 1.322738387 = 0.000000000 0.000000000 + x = -0.877038621 + 1.322738387 x = -0.877038621 + 1.322738387 Combine like terms: -0.877038621 + 1.322738387 = 0.445699766 x = 0.445699766 Simplifying x = 0.445699766Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.199777008, 0.445699766}
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