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Simplifying 11a2 + -12a + -2 = 0 Reorder the terms: -2 + -12a + 11a2 = 0 Solving -2 + -12a + 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'. -0.1818181818 + -1.090909091a + a2 = 0 Move the constant term to the right: Add '0.1818181818' to each side of the equation. -0.1818181818 + -1.090909091a + 0.1818181818 + a2 = 0 + 0.1818181818 Reorder the terms: -0.1818181818 + 0.1818181818 + -1.090909091a + a2 = 0 + 0.1818181818 Combine like terms: -0.1818181818 + 0.1818181818 = 0.0000000000 0.0000000000 + -1.090909091a + a2 = 0 + 0.1818181818 -1.090909091a + a2 = 0 + 0.1818181818 Combine like terms: 0 + 0.1818181818 = 0.1818181818 -1.090909091a + a2 = 0.1818181818 The a term is -1.090909091a. Take half its coefficient (-0.5454545455). Square it (0.2975206612) and add it to both sides. Add '0.2975206612' to each side of the equation. -1.090909091a + 0.2975206612 + a2 = 0.1818181818 + 0.2975206612 Reorder the terms: 0.2975206612 + -1.090909091a + a2 = 0.1818181818 + 0.2975206612 Combine like terms: 0.1818181818 + 0.2975206612 = 0.479338843 0.2975206612 + -1.090909091a + a2 = 0.479338843 Factor a perfect square on the left side: (a + -0.5454545455)(a + -0.5454545455) = 0.479338843 Calculate the square root of the right side: 0.69234301 Break this problem into two subproblems by setting (a + -0.5454545455) equal to 0.69234301 and -0.69234301.Subproblem 1
a + -0.5454545455 = 0.69234301 Simplifying a + -0.5454545455 = 0.69234301 Reorder the terms: -0.5454545455 + a = 0.69234301 Solving -0.5454545455 + a = 0.69234301 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.5454545455' to each side of the equation. -0.5454545455 + 0.5454545455 + a = 0.69234301 + 0.5454545455 Combine like terms: -0.5454545455 + 0.5454545455 = 0.0000000000 0.0000000000 + a = 0.69234301 + 0.5454545455 a = 0.69234301 + 0.5454545455 Combine like terms: 0.69234301 + 0.5454545455 = 1.2377975555 a = 1.2377975555 Simplifying a = 1.2377975555Subproblem 2
a + -0.5454545455 = -0.69234301 Simplifying a + -0.5454545455 = -0.69234301 Reorder the terms: -0.5454545455 + a = -0.69234301 Solving -0.5454545455 + a = -0.69234301 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.5454545455' to each side of the equation. -0.5454545455 + 0.5454545455 + a = -0.69234301 + 0.5454545455 Combine like terms: -0.5454545455 + 0.5454545455 = 0.0000000000 0.0000000000 + a = -0.69234301 + 0.5454545455 a = -0.69234301 + 0.5454545455 Combine like terms: -0.69234301 + 0.5454545455 = -0.1468884645 a = -0.1468884645 Simplifying a = -0.1468884645Solution
The solution to the problem is based on the solutions from the subproblems. a = {1.2377975555, -0.1468884645}
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