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Simplifying a2 + 12a + 13 = 0 Reorder the terms: 13 + 12a + a2 = 0 Solving 13 + 12a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '-13' to each side of the equation. 13 + 12a + -13 + a2 = 0 + -13 Reorder the terms: 13 + -13 + 12a + a2 = 0 + -13 Combine like terms: 13 + -13 = 0 0 + 12a + a2 = 0 + -13 12a + a2 = 0 + -13 Combine like terms: 0 + -13 = -13 12a + a2 = -13 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 = -13 + 36 Reorder the terms: 36 + 12a + a2 = -13 + 36 Combine like terms: -13 + 36 = 23 36 + 12a + a2 = 23 Factor a perfect square on the left side: (a + 6)(a + 6) = 23 Calculate the square root of the right side: 4.795831523 Break this problem into two subproblems by setting (a + 6) equal to 4.795831523 and -4.795831523.Subproblem 1
a + 6 = 4.795831523 Simplifying a + 6 = 4.795831523 Reorder the terms: 6 + a = 4.795831523 Solving 6 + a = 4.795831523 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 = 4.795831523 + -6 Combine like terms: 6 + -6 = 0 0 + a = 4.795831523 + -6 a = 4.795831523 + -6 Combine like terms: 4.795831523 + -6 = -1.204168477 a = -1.204168477 Simplifying a = -1.204168477Subproblem 2
a + 6 = -4.795831523 Simplifying a + 6 = -4.795831523 Reorder the terms: 6 + a = -4.795831523 Solving 6 + a = -4.795831523 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 = -4.795831523 + -6 Combine like terms: 6 + -6 = 0 0 + a = -4.795831523 + -6 a = -4.795831523 + -6 Combine like terms: -4.795831523 + -6 = -10.795831523 a = -10.795831523 Simplifying a = -10.795831523Solution
The solution to the problem is based on the solutions from the subproblems. a = {-1.204168477, -10.795831523}
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