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Simplifying a2 + 12a + 14 = 33 Reorder the terms: 14 + 12a + a2 = 33 Solving 14 + 12a + a2 = 33 Solving for variable 'a'. Reorder the terms: 14 + -33 + 12a + a2 = 33 + -33 Combine like terms: 14 + -33 = -19 -19 + 12a + a2 = 33 + -33 Combine like terms: 33 + -33 = 0 -19 + 12a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '19' to each side of the equation. -19 + 12a + 19 + a2 = 0 + 19 Reorder the terms: -19 + 19 + 12a + a2 = 0 + 19 Combine like terms: -19 + 19 = 0 0 + 12a + a2 = 0 + 19 12a + a2 = 0 + 19 Combine like terms: 0 + 19 = 19 12a + a2 = 19 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 = 19 + 36 Reorder the terms: 36 + 12a + a2 = 19 + 36 Combine like terms: 19 + 36 = 55 36 + 12a + a2 = 55 Factor a perfect square on the left side: (a + 6)(a + 6) = 55 Calculate the square root of the right side: 7.416198487 Break this problem into two subproblems by setting (a + 6) equal to 7.416198487 and -7.416198487.Subproblem 1
a + 6 = 7.416198487 Simplifying a + 6 = 7.416198487 Reorder the terms: 6 + a = 7.416198487 Solving 6 + a = 7.416198487 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 = 7.416198487 + -6 Combine like terms: 6 + -6 = 0 0 + a = 7.416198487 + -6 a = 7.416198487 + -6 Combine like terms: 7.416198487 + -6 = 1.416198487 a = 1.416198487 Simplifying a = 1.416198487Subproblem 2
a + 6 = -7.416198487 Simplifying a + 6 = -7.416198487 Reorder the terms: 6 + a = -7.416198487 Solving 6 + a = -7.416198487 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 = -7.416198487 + -6 Combine like terms: 6 + -6 = 0 0 + a = -7.416198487 + -6 a = -7.416198487 + -6 Combine like terms: -7.416198487 + -6 = -13.416198487 a = -13.416198487 Simplifying a = -13.416198487Solution
The solution to the problem is based on the solutions from the subproblems. a = {1.416198487, -13.416198487}
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