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Simplifying 14x2 + -41x + 5 = 0 Reorder the terms: 5 + -41x + 14x2 = 0 Solving 5 + -41x + 14x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 14 the coefficient of the squared term: Divide each side by '14'. 0.3571428571 + -2.928571429x + x2 = 0 Move the constant term to the right: Add '-0.3571428571' to each side of the equation. 0.3571428571 + -2.928571429x + -0.3571428571 + x2 = 0 + -0.3571428571 Reorder the terms: 0.3571428571 + -0.3571428571 + -2.928571429x + x2 = 0 + -0.3571428571 Combine like terms: 0.3571428571 + -0.3571428571 = 0.0000000000 0.0000000000 + -2.928571429x + x2 = 0 + -0.3571428571 -2.928571429x + x2 = 0 + -0.3571428571 Combine like terms: 0 + -0.3571428571 = -0.3571428571 -2.928571429x + x2 = -0.3571428571 The x term is -2.928571429x. Take half its coefficient (-1.464285715). Square it (2.144132655) and add it to both sides. Add '2.144132655' to each side of the equation. -2.928571429x + 2.144132655 + x2 = -0.3571428571 + 2.144132655 Reorder the terms: 2.144132655 + -2.928571429x + x2 = -0.3571428571 + 2.144132655 Combine like terms: -0.3571428571 + 2.144132655 = 1.7869897979 2.144132655 + -2.928571429x + x2 = 1.7869897979 Factor a perfect square on the left side: (x + -1.464285715)(x + -1.464285715) = 1.7869897979 Calculate the square root of the right side: 1.336783377 Break this problem into two subproblems by setting (x + -1.464285715) equal to 1.336783377 and -1.336783377.Subproblem 1
x + -1.464285715 = 1.336783377 Simplifying x + -1.464285715 = 1.336783377 Reorder the terms: -1.464285715 + x = 1.336783377 Solving -1.464285715 + x = 1.336783377 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.464285715' to each side of the equation. -1.464285715 + 1.464285715 + x = 1.336783377 + 1.464285715 Combine like terms: -1.464285715 + 1.464285715 = 0.000000000 0.000000000 + x = 1.336783377 + 1.464285715 x = 1.336783377 + 1.464285715 Combine like terms: 1.336783377 + 1.464285715 = 2.801069092 x = 2.801069092 Simplifying x = 2.801069092Subproblem 2
x + -1.464285715 = -1.336783377 Simplifying x + -1.464285715 = -1.336783377 Reorder the terms: -1.464285715 + x = -1.336783377 Solving -1.464285715 + x = -1.336783377 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.464285715' to each side of the equation. -1.464285715 + 1.464285715 + x = -1.336783377 + 1.464285715 Combine like terms: -1.464285715 + 1.464285715 = 0.000000000 0.000000000 + x = -1.336783377 + 1.464285715 x = -1.336783377 + 1.464285715 Combine like terms: -1.336783377 + 1.464285715 = 0.127502338 x = 0.127502338 Simplifying x = 0.127502338Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.801069092, 0.127502338}
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