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Simplifying a2 + 12a + -11 = 0 Reorder the terms: -11 + 12a + a2 = 0 Solving -11 + 12a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '11' to each side of the equation. -11 + 12a + 11 + a2 = 0 + 11 Reorder the terms: -11 + 11 + 12a + a2 = 0 + 11 Combine like terms: -11 + 11 = 0 0 + 12a + a2 = 0 + 11 12a + a2 = 0 + 11 Combine like terms: 0 + 11 = 11 12a + a2 = 11 The a term is 12a. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12a + 36 + a2 = 11 + 36 Reorder the terms: 36 + 12a + a2 = 11 + 36 Combine like terms: 11 + 36 = 47 36 + 12a + a2 = 47 Factor a perfect square on the left side: (a + 6)(a + 6) = 47 Calculate the square root of the right side: 6.8556546 Break this problem into two subproblems by setting (a + 6) equal to 6.8556546 and -6.8556546.Subproblem 1
a + 6 = 6.8556546 Simplifying a + 6 = 6.8556546 Reorder the terms: 6 + a = 6.8556546 Solving 6 + a = 6.8556546 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + a = 6.8556546 + -6 Combine like terms: 6 + -6 = 0 0 + a = 6.8556546 + -6 a = 6.8556546 + -6 Combine like terms: 6.8556546 + -6 = 0.8556546 a = 0.8556546 Simplifying a = 0.8556546Subproblem 2
a + 6 = -6.8556546 Simplifying a + 6 = -6.8556546 Reorder the terms: 6 + a = -6.8556546 Solving 6 + a = -6.8556546 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + a = -6.8556546 + -6 Combine like terms: 6 + -6 = 0 0 + a = -6.8556546 + -6 a = -6.8556546 + -6 Combine like terms: -6.8556546 + -6 = -12.8556546 a = -12.8556546 Simplifying a = -12.8556546Solution
The solution to the problem is based on the solutions from the subproblems. a = {0.8556546, -12.8556546}
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