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Simplifying 11a2 + -6a + -20 = 0 Reorder the terms: -20 + -6a + 11a2 = 0 Solving -20 + -6a + 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 + -0.5454545455a + a2 = 0 Move the constant term to the right: Add '1.818181818' to each side of the equation. -1.818181818 + -0.5454545455a + 1.818181818 + a2 = 0 + 1.818181818 Reorder the terms: -1.818181818 + 1.818181818 + -0.5454545455a + a2 = 0 + 1.818181818 Combine like terms: -1.818181818 + 1.818181818 = 0.000000000 0.000000000 + -0.5454545455a + a2 = 0 + 1.818181818 -0.5454545455a + a2 = 0 + 1.818181818 Combine like terms: 0 + 1.818181818 = 1.818181818 -0.5454545455a + a2 = 1.818181818 The a term is -0.5454545455a. Take half its coefficient (-0.2727272728). Square it (0.07438016533) and add it to both sides. Add '0.07438016533' to each side of the equation. -0.5454545455a + 0.07438016533 + a2 = 1.818181818 + 0.07438016533 Reorder the terms: 0.07438016533 + -0.5454545455a + a2 = 1.818181818 + 0.07438016533 Combine like terms: 1.818181818 + 0.07438016533 = 1.89256198333 0.07438016533 + -0.5454545455a + a2 = 1.89256198333 Factor a perfect square on the left side: (a + -0.2727272728)(a + -0.2727272728) = 1.89256198333 Calculate the square root of the right side: 1.375704177 Break this problem into two subproblems by setting (a + -0.2727272728) equal to 1.375704177 and -1.375704177.Subproblem 1
a + -0.2727272728 = 1.375704177 Simplifying a + -0.2727272728 = 1.375704177 Reorder the terms: -0.2727272728 + a = 1.375704177 Solving -0.2727272728 + a = 1.375704177 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.2727272728' to each side of the equation. -0.2727272728 + 0.2727272728 + a = 1.375704177 + 0.2727272728 Combine like terms: -0.2727272728 + 0.2727272728 = 0.0000000000 0.0000000000 + a = 1.375704177 + 0.2727272728 a = 1.375704177 + 0.2727272728 Combine like terms: 1.375704177 + 0.2727272728 = 1.6484314498 a = 1.6484314498 Simplifying a = 1.6484314498Subproblem 2
a + -0.2727272728 = -1.375704177 Simplifying a + -0.2727272728 = -1.375704177 Reorder the terms: -0.2727272728 + a = -1.375704177 Solving -0.2727272728 + a = -1.375704177 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.2727272728' to each side of the equation. -0.2727272728 + 0.2727272728 + a = -1.375704177 + 0.2727272728 Combine like terms: -0.2727272728 + 0.2727272728 = 0.0000000000 0.0000000000 + a = -1.375704177 + 0.2727272728 a = -1.375704177 + 0.2727272728 Combine like terms: -1.375704177 + 0.2727272728 = -1.1029769042 a = -1.1029769042 Simplifying a = -1.1029769042Solution
The solution to the problem is based on the solutions from the subproblems. a = {1.6484314498, -1.1029769042}
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