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Simplifying 7a2 + -24a + -4 = 0 Reorder the terms: -4 + -24a + 7a2 = 0 Solving -4 + -24a + 7a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.5714285714 + -3.428571429a + a2 = 0 Move the constant term to the right: Add '0.5714285714' to each side of the equation. -0.5714285714 + -3.428571429a + 0.5714285714 + a2 = 0 + 0.5714285714 Reorder the terms: -0.5714285714 + 0.5714285714 + -3.428571429a + a2 = 0 + 0.5714285714 Combine like terms: -0.5714285714 + 0.5714285714 = 0.0000000000 0.0000000000 + -3.428571429a + a2 = 0 + 0.5714285714 -3.428571429a + a2 = 0 + 0.5714285714 Combine like terms: 0 + 0.5714285714 = 0.5714285714 -3.428571429a + a2 = 0.5714285714 The a term is -3.428571429a. 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. -3.428571429a + 2.938775513 + a2 = 0.5714285714 + 2.938775513 Reorder the terms: 2.938775513 + -3.428571429a + a2 = 0.5714285714 + 2.938775513 Combine like terms: 0.5714285714 + 2.938775513 = 3.5102040844 2.938775513 + -3.428571429a + a2 = 3.5102040844 Factor a perfect square on the left side: (a + -1.714285715)(a + -1.714285715) = 3.5102040844 Calculate the square root of the right side: 1.873553865 Break this problem into two subproblems by setting (a + -1.714285715) equal to 1.873553865 and -1.873553865.Subproblem 1
a + -1.714285715 = 1.873553865 Simplifying a + -1.714285715 = 1.873553865 Reorder the terms: -1.714285715 + a = 1.873553865 Solving -1.714285715 + a = 1.873553865 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '1.714285715' to each side of the equation. -1.714285715 + 1.714285715 + a = 1.873553865 + 1.714285715 Combine like terms: -1.714285715 + 1.714285715 = 0.000000000 0.000000000 + a = 1.873553865 + 1.714285715 a = 1.873553865 + 1.714285715 Combine like terms: 1.873553865 + 1.714285715 = 3.58783958 a = 3.58783958 Simplifying a = 3.58783958Subproblem 2
a + -1.714285715 = -1.873553865 Simplifying a + -1.714285715 = -1.873553865 Reorder the terms: -1.714285715 + a = -1.873553865 Solving -1.714285715 + a = -1.873553865 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '1.714285715' to each side of the equation. -1.714285715 + 1.714285715 + a = -1.873553865 + 1.714285715 Combine like terms: -1.714285715 + 1.714285715 = 0.000000000 0.000000000 + a = -1.873553865 + 1.714285715 a = -1.873553865 + 1.714285715 Combine like terms: -1.873553865 + 1.714285715 = -0.15926815 a = -0.15926815 Simplifying a = -0.15926815Solution
The solution to the problem is based on the solutions from the subproblems. a = {3.58783958, -0.15926815}
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