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Simplifying a2 + 12a = 3 Reorder the terms: 12a + a2 = 3 Solving 12a + a2 = 3 Solving for variable 'a'. Reorder the terms: -3 + 12a + a2 = 3 + -3 Combine like terms: 3 + -3 = 0 -3 + 12a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '3' to each side of the equation. -3 + 12a + 3 + a2 = 0 + 3 Reorder the terms: -3 + 3 + 12a + a2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 12a + a2 = 0 + 3 12a + a2 = 0 + 3 Combine like terms: 0 + 3 = 3 12a + a2 = 3 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 = 3 + 36 Reorder the terms: 36 + 12a + a2 = 3 + 36 Combine like terms: 3 + 36 = 39 36 + 12a + a2 = 39 Factor a perfect square on the left side: (a + 6)(a + 6) = 39 Calculate the square root of the right side: 6.244997998 Break this problem into two subproblems by setting (a + 6) equal to 6.244997998 and -6.244997998.Subproblem 1
a + 6 = 6.244997998 Simplifying a + 6 = 6.244997998 Reorder the terms: 6 + a = 6.244997998 Solving 6 + a = 6.244997998 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 = 6.244997998 + -6 Combine like terms: 6 + -6 = 0 0 + a = 6.244997998 + -6 a = 6.244997998 + -6 Combine like terms: 6.244997998 + -6 = 0.244997998 a = 0.244997998 Simplifying a = 0.244997998Subproblem 2
a + 6 = -6.244997998 Simplifying a + 6 = -6.244997998 Reorder the terms: 6 + a = -6.244997998 Solving 6 + a = -6.244997998 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 = -6.244997998 + -6 Combine like terms: 6 + -6 = 0 0 + a = -6.244997998 + -6 a = -6.244997998 + -6 Combine like terms: -6.244997998 + -6 = -12.244997998 a = -12.244997998 Simplifying a = -12.244997998Solution
The solution to the problem is based on the solutions from the subproblems. a = {0.244997998, -12.244997998}
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