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Simplifying 7x2 + -24x + 1 = 0 Reorder the terms: 1 + -24x + 7x2 = 0 Solving 1 + -24x + 7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 0.1428571429 + -3.428571429x + x2 = 0 Move the constant term to the right: Add '-0.1428571429' to each side of the equation. 0.1428571429 + -3.428571429x + -0.1428571429 + x2 = 0 + -0.1428571429 Reorder the terms: 0.1428571429 + -0.1428571429 + -3.428571429x + x2 = 0 + -0.1428571429 Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000 0.0000000000 + -3.428571429x + x2 = 0 + -0.1428571429 -3.428571429x + x2 = 0 + -0.1428571429 Combine like terms: 0 + -0.1428571429 = -0.1428571429 -3.428571429x + x2 = -0.1428571429 The x term is -3.428571429x. Take half its coefficient (-1.714285715). Square it (2.938775513) and add it to both sides. Add '2.938775513' to each side of the equation. -3.428571429x + 2.938775513 + x2 = -0.1428571429 + 2.938775513 Reorder the terms: 2.938775513 + -3.428571429x + x2 = -0.1428571429 + 2.938775513 Combine like terms: -0.1428571429 + 2.938775513 = 2.7959183701 2.938775513 + -3.428571429x + x2 = 2.7959183701 Factor a perfect square on the left side: (x + -1.714285715)(x + -1.714285715) = 2.7959183701 Calculate the square root of the right side: 1.672099988 Break this problem into two subproblems by setting (x + -1.714285715) equal to 1.672099988 and -1.672099988.Subproblem 1
x + -1.714285715 = 1.672099988 Simplifying x + -1.714285715 = 1.672099988 Reorder the terms: -1.714285715 + x = 1.672099988 Solving -1.714285715 + x = 1.672099988 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.714285715' to each side of the equation. -1.714285715 + 1.714285715 + x = 1.672099988 + 1.714285715 Combine like terms: -1.714285715 + 1.714285715 = 0.000000000 0.000000000 + x = 1.672099988 + 1.714285715 x = 1.672099988 + 1.714285715 Combine like terms: 1.672099988 + 1.714285715 = 3.386385703 x = 3.386385703 Simplifying x = 3.386385703Subproblem 2
x + -1.714285715 = -1.672099988 Simplifying x + -1.714285715 = -1.672099988 Reorder the terms: -1.714285715 + x = -1.672099988 Solving -1.714285715 + x = -1.672099988 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.714285715' to each side of the equation. -1.714285715 + 1.714285715 + x = -1.672099988 + 1.714285715 Combine like terms: -1.714285715 + 1.714285715 = 0.000000000 0.000000000 + x = -1.672099988 + 1.714285715 x = -1.672099988 + 1.714285715 Combine like terms: -1.672099988 + 1.714285715 = 0.042185727 x = 0.042185727 Simplifying x = 0.042185727Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.386385703, 0.042185727}
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