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Simplifying 8a2 + 35a + -44 = 0 Reorder the terms: -44 + 35a + 8a2 = 0 Solving -44 + 35a + 8a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -5.5 + 4.375a + a2 = 0 Move the constant term to the right: Add '5.5' to each side of the equation. -5.5 + 4.375a + 5.5 + a2 = 0 + 5.5 Reorder the terms: -5.5 + 5.5 + 4.375a + a2 = 0 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + 4.375a + a2 = 0 + 5.5 4.375a + a2 = 0 + 5.5 Combine like terms: 0 + 5.5 = 5.5 4.375a + a2 = 5.5 The a term is 4.375a. Take half its coefficient (2.1875). Square it (4.78515625) and add it to both sides. Add '4.78515625' to each side of the equation. 4.375a + 4.78515625 + a2 = 5.5 + 4.78515625 Reorder the terms: 4.78515625 + 4.375a + a2 = 5.5 + 4.78515625 Combine like terms: 5.5 + 4.78515625 = 10.28515625 4.78515625 + 4.375a + a2 = 10.28515625 Factor a perfect square on the left side: (a + 2.1875)(a + 2.1875) = 10.28515625 Calculate the square root of the right side: 3.207047903 Break this problem into two subproblems by setting (a + 2.1875) equal to 3.207047903 and -3.207047903.Subproblem 1
a + 2.1875 = 3.207047903 Simplifying a + 2.1875 = 3.207047903 Reorder the terms: 2.1875 + a = 3.207047903 Solving 2.1875 + a = 3.207047903 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-2.1875' to each side of the equation. 2.1875 + -2.1875 + a = 3.207047903 + -2.1875 Combine like terms: 2.1875 + -2.1875 = 0.0000 0.0000 + a = 3.207047903 + -2.1875 a = 3.207047903 + -2.1875 Combine like terms: 3.207047903 + -2.1875 = 1.019547903 a = 1.019547903 Simplifying a = 1.019547903Subproblem 2
a + 2.1875 = -3.207047903 Simplifying a + 2.1875 = -3.207047903 Reorder the terms: 2.1875 + a = -3.207047903 Solving 2.1875 + a = -3.207047903 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-2.1875' to each side of the equation. 2.1875 + -2.1875 + a = -3.207047903 + -2.1875 Combine like terms: 2.1875 + -2.1875 = 0.0000 0.0000 + a = -3.207047903 + -2.1875 a = -3.207047903 + -2.1875 Combine like terms: -3.207047903 + -2.1875 = -5.394547903 a = -5.394547903 Simplifying a = -5.394547903Solution
The solution to the problem is based on the solutions from the subproblems. a = {1.019547903, -5.394547903}
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