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Simplifying a2 + 12a + -27 = 0 Reorder the terms: -27 + 12a + a2 = 0 Solving -27 + 12a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '27' to each side of the equation. -27 + 12a + 27 + a2 = 0 + 27 Reorder the terms: -27 + 27 + 12a + a2 = 0 + 27 Combine like terms: -27 + 27 = 0 0 + 12a + a2 = 0 + 27 12a + a2 = 0 + 27 Combine like terms: 0 + 27 = 27 12a + a2 = 27 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 = 27 + 36 Reorder the terms: 36 + 12a + a2 = 27 + 36 Combine like terms: 27 + 36 = 63 36 + 12a + a2 = 63 Factor a perfect square on the left side: (a + 6)(a + 6) = 63 Calculate the square root of the right side: 7.937253933 Break this problem into two subproblems by setting (a + 6) equal to 7.937253933 and -7.937253933.Subproblem 1
a + 6 = 7.937253933 Simplifying a + 6 = 7.937253933 Reorder the terms: 6 + a = 7.937253933 Solving 6 + a = 7.937253933 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 = 7.937253933 + -6 Combine like terms: 6 + -6 = 0 0 + a = 7.937253933 + -6 a = 7.937253933 + -6 Combine like terms: 7.937253933 + -6 = 1.937253933 a = 1.937253933 Simplifying a = 1.937253933Subproblem 2
a + 6 = -7.937253933 Simplifying a + 6 = -7.937253933 Reorder the terms: 6 + a = -7.937253933 Solving 6 + a = -7.937253933 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 = -7.937253933 + -6 Combine like terms: 6 + -6 = 0 0 + a = -7.937253933 + -6 a = -7.937253933 + -6 Combine like terms: -7.937253933 + -6 = -13.937253933 a = -13.937253933 Simplifying a = -13.937253933Solution
The solution to the problem is based on the solutions from the subproblems. a = {1.937253933, -13.937253933}
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