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Simplifying 7x2 + 24x + -2 = 0 Reorder the terms: -2 + 24x + 7x2 = 0 Solving -2 + 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'. -0.2857142857 + 3.428571429x + x2 = 0 Move the constant term to the right: Add '0.2857142857' to each side of the equation. -0.2857142857 + 3.428571429x + 0.2857142857 + x2 = 0 + 0.2857142857 Reorder the terms: -0.2857142857 + 0.2857142857 + 3.428571429x + x2 = 0 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + 3.428571429x + x2 = 0 + 0.2857142857 3.428571429x + x2 = 0 + 0.2857142857 Combine like terms: 0 + 0.2857142857 = 0.2857142857 3.428571429x + x2 = 0.2857142857 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 = 0.2857142857 + 2.938775513 Reorder the terms: 2.938775513 + 3.428571429x + x2 = 0.2857142857 + 2.938775513 Combine like terms: 0.2857142857 + 2.938775513 = 3.2244897987 2.938775513 + 3.428571429x + x2 = 3.2244897987 Factor a perfect square on the left side: (x + 1.714285715)(x + 1.714285715) = 3.2244897987 Calculate the square root of the right side: 1.795686442 Break this problem into two subproblems by setting (x + 1.714285715) equal to 1.795686442 and -1.795686442.Subproblem 1
x + 1.714285715 = 1.795686442 Simplifying x + 1.714285715 = 1.795686442 Reorder the terms: 1.714285715 + x = 1.795686442 Solving 1.714285715 + x = 1.795686442 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 = 1.795686442 + -1.714285715 Combine like terms: 1.714285715 + -1.714285715 = 0.000000000 0.000000000 + x = 1.795686442 + -1.714285715 x = 1.795686442 + -1.714285715 Combine like terms: 1.795686442 + -1.714285715 = 0.081400727 x = 0.081400727 Simplifying x = 0.081400727Subproblem 2
x + 1.714285715 = -1.795686442 Simplifying x + 1.714285715 = -1.795686442 Reorder the terms: 1.714285715 + x = -1.795686442 Solving 1.714285715 + x = -1.795686442 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 = -1.795686442 + -1.714285715 Combine like terms: 1.714285715 + -1.714285715 = 0.000000000 0.000000000 + x = -1.795686442 + -1.714285715 x = -1.795686442 + -1.714285715 Combine like terms: -1.795686442 + -1.714285715 = -3.509972157 x = -3.509972157 Simplifying x = -3.509972157Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.081400727, -3.509972157}
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