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Simplifying a2 = -12a + 66 Reorder the terms: a2 = 66 + -12a Solving a2 = 66 + -12a Solving for variable 'a'. Reorder the terms: -66 + 12a + a2 = 66 + -12a + -66 + 12a Reorder the terms: -66 + 12a + a2 = 66 + -66 + -12a + 12a Combine like terms: 66 + -66 = 0 -66 + 12a + a2 = 0 + -12a + 12a -66 + 12a + a2 = -12a + 12a Combine like terms: -12a + 12a = 0 -66 + 12a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '66' to each side of the equation. -66 + 12a + 66 + a2 = 0 + 66 Reorder the terms: -66 + 66 + 12a + a2 = 0 + 66 Combine like terms: -66 + 66 = 0 0 + 12a + a2 = 0 + 66 12a + a2 = 0 + 66 Combine like terms: 0 + 66 = 66 12a + a2 = 66 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 = 66 + 36 Reorder the terms: 36 + 12a + a2 = 66 + 36 Combine like terms: 66 + 36 = 102 36 + 12a + a2 = 102 Factor a perfect square on the left side: (a + 6)(a + 6) = 102 Calculate the square root of the right side: 10.099504938 Break this problem into two subproblems by setting (a + 6) equal to 10.099504938 and -10.099504938.Subproblem 1
a + 6 = 10.099504938 Simplifying a + 6 = 10.099504938 Reorder the terms: 6 + a = 10.099504938 Solving 6 + a = 10.099504938 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 = 10.099504938 + -6 Combine like terms: 6 + -6 = 0 0 + a = 10.099504938 + -6 a = 10.099504938 + -6 Combine like terms: 10.099504938 + -6 = 4.099504938 a = 4.099504938 Simplifying a = 4.099504938Subproblem 2
a + 6 = -10.099504938 Simplifying a + 6 = -10.099504938 Reorder the terms: 6 + a = -10.099504938 Solving 6 + a = -10.099504938 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 = -10.099504938 + -6 Combine like terms: 6 + -6 = 0 0 + a = -10.099504938 + -6 a = -10.099504938 + -6 Combine like terms: -10.099504938 + -6 = -16.099504938 a = -16.099504938 Simplifying a = -16.099504938Solution
The solution to the problem is based on the solutions from the subproblems. a = {4.099504938, -16.099504938}
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