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Simplifying 11a2 + -4a + -13 = 0 Reorder the terms: -13 + -4a + 11a2 = 0 Solving -13 + -4a + 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'. -1.181818182 + -0.3636363636a + a2 = 0 Move the constant term to the right: Add '1.181818182' to each side of the equation. -1.181818182 + -0.3636363636a + 1.181818182 + a2 = 0 + 1.181818182 Reorder the terms: -1.181818182 + 1.181818182 + -0.3636363636a + a2 = 0 + 1.181818182 Combine like terms: -1.181818182 + 1.181818182 = 0.000000000 0.000000000 + -0.3636363636a + a2 = 0 + 1.181818182 -0.3636363636a + a2 = 0 + 1.181818182 Combine like terms: 0 + 1.181818182 = 1.181818182 -0.3636363636a + a2 = 1.181818182 The a term is -0.3636363636a. Take half its coefficient (-0.1818181818). Square it (0.03305785123) and add it to both sides. Add '0.03305785123' to each side of the equation. -0.3636363636a + 0.03305785123 + a2 = 1.181818182 + 0.03305785123 Reorder the terms: 0.03305785123 + -0.3636363636a + a2 = 1.181818182 + 0.03305785123 Combine like terms: 1.181818182 + 0.03305785123 = 1.21487603323 0.03305785123 + -0.3636363636a + a2 = 1.21487603323 Factor a perfect square on the left side: (a + -0.1818181818)(a + -0.1818181818) = 1.21487603323 Calculate the square root of the right side: 1.10221415 Break this problem into two subproblems by setting (a + -0.1818181818) equal to 1.10221415 and -1.10221415.Subproblem 1
a + -0.1818181818 = 1.10221415 Simplifying a + -0.1818181818 = 1.10221415 Reorder the terms: -0.1818181818 + a = 1.10221415 Solving -0.1818181818 + a = 1.10221415 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.1818181818' to each side of the equation. -0.1818181818 + 0.1818181818 + a = 1.10221415 + 0.1818181818 Combine like terms: -0.1818181818 + 0.1818181818 = 0.0000000000 0.0000000000 + a = 1.10221415 + 0.1818181818 a = 1.10221415 + 0.1818181818 Combine like terms: 1.10221415 + 0.1818181818 = 1.2840323318 a = 1.2840323318 Simplifying a = 1.2840323318Subproblem 2
a + -0.1818181818 = -1.10221415 Simplifying a + -0.1818181818 = -1.10221415 Reorder the terms: -0.1818181818 + a = -1.10221415 Solving -0.1818181818 + a = -1.10221415 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.1818181818' to each side of the equation. -0.1818181818 + 0.1818181818 + a = -1.10221415 + 0.1818181818 Combine like terms: -0.1818181818 + 0.1818181818 = 0.0000000000 0.0000000000 + a = -1.10221415 + 0.1818181818 a = -1.10221415 + 0.1818181818 Combine like terms: -1.10221415 + 0.1818181818 = -0.9203959682 a = -0.9203959682 Simplifying a = -0.9203959682Solution
The solution to the problem is based on the solutions from the subproblems. a = {1.2840323318, -0.9203959682}
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