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Simplifying 41x2 + 11x + -10 = 0 Reorder the terms: -10 + 11x + 41x2 = 0 Solving -10 + 11x + 41x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 41 the coefficient of the squared term: Divide each side by '41'. -0.243902439 + 0.2682926829x + x2 = 0 Move the constant term to the right: Add '0.243902439' to each side of the equation. -0.243902439 + 0.2682926829x + 0.243902439 + x2 = 0 + 0.243902439 Reorder the terms: -0.243902439 + 0.243902439 + 0.2682926829x + x2 = 0 + 0.243902439 Combine like terms: -0.243902439 + 0.243902439 = 0.000000000 0.000000000 + 0.2682926829x + x2 = 0 + 0.243902439 0.2682926829x + x2 = 0 + 0.243902439 Combine like terms: 0 + 0.243902439 = 0.243902439 0.2682926829x + x2 = 0.243902439 The x term is 0.2682926829x. Take half its coefficient (0.1341463415). Square it (0.01799524094) and add it to both sides. Add '0.01799524094' to each side of the equation. 0.2682926829x + 0.01799524094 + x2 = 0.243902439 + 0.01799524094 Reorder the terms: 0.01799524094 + 0.2682926829x + x2 = 0.243902439 + 0.01799524094 Combine like terms: 0.243902439 + 0.01799524094 = 0.26189767994 0.01799524094 + 0.2682926829x + x2 = 0.26189767994 Factor a perfect square on the left side: (x + 0.1341463415)(x + 0.1341463415) = 0.26189767994 Calculate the square root of the right side: 0.511759397 Break this problem into two subproblems by setting (x + 0.1341463415) equal to 0.511759397 and -0.511759397.Subproblem 1
x + 0.1341463415 = 0.511759397 Simplifying x + 0.1341463415 = 0.511759397 Reorder the terms: 0.1341463415 + x = 0.511759397 Solving 0.1341463415 + x = 0.511759397 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1341463415' to each side of the equation. 0.1341463415 + -0.1341463415 + x = 0.511759397 + -0.1341463415 Combine like terms: 0.1341463415 + -0.1341463415 = 0.0000000000 0.0000000000 + x = 0.511759397 + -0.1341463415 x = 0.511759397 + -0.1341463415 Combine like terms: 0.511759397 + -0.1341463415 = 0.3776130555 x = 0.3776130555 Simplifying x = 0.3776130555Subproblem 2
x + 0.1341463415 = -0.511759397 Simplifying x + 0.1341463415 = -0.511759397 Reorder the terms: 0.1341463415 + x = -0.511759397 Solving 0.1341463415 + x = -0.511759397 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1341463415' to each side of the equation. 0.1341463415 + -0.1341463415 + x = -0.511759397 + -0.1341463415 Combine like terms: 0.1341463415 + -0.1341463415 = 0.0000000000 0.0000000000 + x = -0.511759397 + -0.1341463415 x = -0.511759397 + -0.1341463415 Combine like terms: -0.511759397 + -0.1341463415 = -0.6459057385 x = -0.6459057385 Simplifying x = -0.6459057385Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.3776130555, -0.6459057385}
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