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Simplifying 11a2 + 8a + -20 = 0 Reorder the terms: -20 + 8a + 11a2 = 0 Solving -20 + 8a + 11a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -1.818181818 + 0.7272727273a + a2 = 0 Move the constant term to the right: Add '1.818181818' to each side of the equation. -1.818181818 + 0.7272727273a + 1.818181818 + a2 = 0 + 1.818181818 Reorder the terms: -1.818181818 + 1.818181818 + 0.7272727273a + a2 = 0 + 1.818181818 Combine like terms: -1.818181818 + 1.818181818 = 0.000000000 0.000000000 + 0.7272727273a + a2 = 0 + 1.818181818 0.7272727273a + a2 = 0 + 1.818181818 Combine like terms: 0 + 1.818181818 = 1.818181818 0.7272727273a + a2 = 1.818181818 The a term is 0.7272727273a. Take half its coefficient (0.3636363637). Square it (0.1322314050) and add it to both sides. Add '0.1322314050' to each side of the equation. 0.7272727273a + 0.1322314050 + a2 = 1.818181818 + 0.1322314050 Reorder the terms: 0.1322314050 + 0.7272727273a + a2 = 1.818181818 + 0.1322314050 Combine like terms: 1.818181818 + 0.1322314050 = 1.950413223 0.1322314050 + 0.7272727273a + a2 = 1.950413223 Factor a perfect square on the left side: (a + 0.3636363637)(a + 0.3636363637) = 1.950413223 Calculate the square root of the right side: 1.396571954 Break this problem into two subproblems by setting (a + 0.3636363637) equal to 1.396571954 and -1.396571954.Subproblem 1
a + 0.3636363637 = 1.396571954 Simplifying a + 0.3636363637 = 1.396571954 Reorder the terms: 0.3636363637 + a = 1.396571954 Solving 0.3636363637 + a = 1.396571954 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.3636363637' to each side of the equation. 0.3636363637 + -0.3636363637 + a = 1.396571954 + -0.3636363637 Combine like terms: 0.3636363637 + -0.3636363637 = 0.0000000000 0.0000000000 + a = 1.396571954 + -0.3636363637 a = 1.396571954 + -0.3636363637 Combine like terms: 1.396571954 + -0.3636363637 = 1.0329355903 a = 1.0329355903 Simplifying a = 1.0329355903Subproblem 2
a + 0.3636363637 = -1.396571954 Simplifying a + 0.3636363637 = -1.396571954 Reorder the terms: 0.3636363637 + a = -1.396571954 Solving 0.3636363637 + a = -1.396571954 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.3636363637' to each side of the equation. 0.3636363637 + -0.3636363637 + a = -1.396571954 + -0.3636363637 Combine like terms: 0.3636363637 + -0.3636363637 = 0.0000000000 0.0000000000 + a = -1.396571954 + -0.3636363637 a = -1.396571954 + -0.3636363637 Combine like terms: -1.396571954 + -0.3636363637 = -1.7602083177 a = -1.7602083177 Simplifying a = -1.7602083177Solution
The solution to the problem is based on the solutions from the subproblems. a = {1.0329355903, -1.7602083177}
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