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Simplifying 8a2 + -5a + -8 = 0 Reorder the terms: -8 + -5a + 8a2 = 0 Solving -8 + -5a + 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'. -1 + -0.625a + a2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -0.625a + 1 + a2 = 0 + 1 Reorder the terms: -1 + 1 + -0.625a + a2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -0.625a + a2 = 0 + 1 -0.625a + a2 = 0 + 1 Combine like terms: 0 + 1 = 1 -0.625a + a2 = 1 The a term is -0.625a. Take half its coefficient (-0.3125). Square it (0.09765625) and add it to both sides. Add '0.09765625' to each side of the equation. -0.625a + 0.09765625 + a2 = 1 + 0.09765625 Reorder the terms: 0.09765625 + -0.625a + a2 = 1 + 0.09765625 Combine like terms: 1 + 0.09765625 = 1.09765625 0.09765625 + -0.625a + a2 = 1.09765625 Factor a perfect square on the left side: (a + -0.3125)(a + -0.3125) = 1.09765625 Calculate the square root of the right side: 1.047690913 Break this problem into two subproblems by setting (a + -0.3125) equal to 1.047690913 and -1.047690913.Subproblem 1
a + -0.3125 = 1.047690913 Simplifying a + -0.3125 = 1.047690913 Reorder the terms: -0.3125 + a = 1.047690913 Solving -0.3125 + a = 1.047690913 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.3125' to each side of the equation. -0.3125 + 0.3125 + a = 1.047690913 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + a = 1.047690913 + 0.3125 a = 1.047690913 + 0.3125 Combine like terms: 1.047690913 + 0.3125 = 1.360190913 a = 1.360190913 Simplifying a = 1.360190913Subproblem 2
a + -0.3125 = -1.047690913 Simplifying a + -0.3125 = -1.047690913 Reorder the terms: -0.3125 + a = -1.047690913 Solving -0.3125 + a = -1.047690913 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.3125' to each side of the equation. -0.3125 + 0.3125 + a = -1.047690913 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + a = -1.047690913 + 0.3125 a = -1.047690913 + 0.3125 Combine like terms: -1.047690913 + 0.3125 = -0.735190913 a = -0.735190913 Simplifying a = -0.735190913Solution
The solution to the problem is based on the solutions from the subproblems. a = {1.360190913, -0.735190913}
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