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Simplifying 8a2 + -26a + -9 = 0 Reorder the terms: -9 + -26a + 8a2 = 0 Solving -9 + -26a + 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'. -1.125 + -3.25a + a2 = 0 Move the constant term to the right: Add '1.125' to each side of the equation. -1.125 + -3.25a + 1.125 + a2 = 0 + 1.125 Reorder the terms: -1.125 + 1.125 + -3.25a + a2 = 0 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + -3.25a + a2 = 0 + 1.125 -3.25a + a2 = 0 + 1.125 Combine like terms: 0 + 1.125 = 1.125 -3.25a + a2 = 1.125 The a term is -3.25a. Take half its coefficient (-1.625). Square it (2.640625) and add it to both sides. Add '2.640625' to each side of the equation. -3.25a + 2.640625 + a2 = 1.125 + 2.640625 Reorder the terms: 2.640625 + -3.25a + a2 = 1.125 + 2.640625 Combine like terms: 1.125 + 2.640625 = 3.765625 2.640625 + -3.25a + a2 = 3.765625 Factor a perfect square on the left side: (a + -1.625)(a + -1.625) = 3.765625 Calculate the square root of the right side: 1.940521837 Break this problem into two subproblems by setting (a + -1.625) equal to 1.940521837 and -1.940521837.Subproblem 1
a + -1.625 = 1.940521837 Simplifying a + -1.625 = 1.940521837 Reorder the terms: -1.625 + a = 1.940521837 Solving -1.625 + a = 1.940521837 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '1.625' to each side of the equation. -1.625 + 1.625 + a = 1.940521837 + 1.625 Combine like terms: -1.625 + 1.625 = 0.000 0.000 + a = 1.940521837 + 1.625 a = 1.940521837 + 1.625 Combine like terms: 1.940521837 + 1.625 = 3.565521837 a = 3.565521837 Simplifying a = 3.565521837Subproblem 2
a + -1.625 = -1.940521837 Simplifying a + -1.625 = -1.940521837 Reorder the terms: -1.625 + a = -1.940521837 Solving -1.625 + a = -1.940521837 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '1.625' to each side of the equation. -1.625 + 1.625 + a = -1.940521837 + 1.625 Combine like terms: -1.625 + 1.625 = 0.000 0.000 + a = -1.940521837 + 1.625 a = -1.940521837 + 1.625 Combine like terms: -1.940521837 + 1.625 = -0.315521837 a = -0.315521837 Simplifying a = -0.315521837Solution
The solution to the problem is based on the solutions from the subproblems. a = {3.565521837, -0.315521837}
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