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Simplifying 11a2 + -4 = 12a Reorder the terms: -4 + 11a2 = 12a Solving -4 + 11a2 = 12a Solving for variable 'a'. Reorder the terms: -4 + -12a + 11a2 = 12a + -12a Combine like terms: 12a + -12a = 0 -4 + -12a + 11a2 = 0 Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -0.3636363636 + -1.090909091a + a2 = 0 Move the constant term to the right: Add '0.3636363636' to each side of the equation. -0.3636363636 + -1.090909091a + 0.3636363636 + a2 = 0 + 0.3636363636 Reorder the terms: -0.3636363636 + 0.3636363636 + -1.090909091a + a2 = 0 + 0.3636363636 Combine like terms: -0.3636363636 + 0.3636363636 = 0.0000000000 0.0000000000 + -1.090909091a + a2 = 0 + 0.3636363636 -1.090909091a + a2 = 0 + 0.3636363636 Combine like terms: 0 + 0.3636363636 = 0.3636363636 -1.090909091a + a2 = 0.3636363636 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 = 0.3636363636 + 0.2975206612 Reorder the terms: 0.2975206612 + -1.090909091a + a2 = 0.3636363636 + 0.2975206612 Combine like terms: 0.3636363636 + 0.2975206612 = 0.6611570248 0.2975206612 + -1.090909091a + a2 = 0.6611570248 Factor a perfect square on the left side: (a + -0.5454545455)(a + -0.5454545455) = 0.6611570248 Calculate the square root of the right side: 0.813115628 Break this problem into two subproblems by setting (a + -0.5454545455) equal to 0.813115628 and -0.813115628.Subproblem 1
a + -0.5454545455 = 0.813115628 Simplifying a + -0.5454545455 = 0.813115628 Reorder the terms: -0.5454545455 + a = 0.813115628 Solving -0.5454545455 + a = 0.813115628 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 = 0.813115628 + 0.5454545455 Combine like terms: -0.5454545455 + 0.5454545455 = 0.0000000000 0.0000000000 + a = 0.813115628 + 0.5454545455 a = 0.813115628 + 0.5454545455 Combine like terms: 0.813115628 + 0.5454545455 = 1.3585701735 a = 1.3585701735 Simplifying a = 1.3585701735Subproblem 2
a + -0.5454545455 = -0.813115628 Simplifying a + -0.5454545455 = -0.813115628 Reorder the terms: -0.5454545455 + a = -0.813115628 Solving -0.5454545455 + a = -0.813115628 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 = -0.813115628 + 0.5454545455 Combine like terms: -0.5454545455 + 0.5454545455 = 0.0000000000 0.0000000000 + a = -0.813115628 + 0.5454545455 a = -0.813115628 + 0.5454545455 Combine like terms: -0.813115628 + 0.5454545455 = -0.2676610825 a = -0.2676610825 Simplifying a = -0.2676610825Solution
The solution to the problem is based on the solutions from the subproblems. a = {1.3585701735, -0.2676610825}
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