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Simplifying a2 + 14a + 12 = 8 Reorder the terms: 12 + 14a + a2 = 8 Solving 12 + 14a + a2 = 8 Solving for variable 'a'. Reorder the terms: 12 + -8 + 14a + a2 = 8 + -8 Combine like terms: 12 + -8 = 4 4 + 14a + a2 = 8 + -8 Combine like terms: 8 + -8 = 0 4 + 14a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '-4' to each side of the equation. 4 + 14a + -4 + a2 = 0 + -4 Reorder the terms: 4 + -4 + 14a + a2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 14a + a2 = 0 + -4 14a + a2 = 0 + -4 Combine like terms: 0 + -4 = -4 14a + a2 = -4 The a term is 14a. Take half its coefficient (7). Square it (49) and add it to both sides. Add '49' to each side of the equation. 14a + 49 + a2 = -4 + 49 Reorder the terms: 49 + 14a + a2 = -4 + 49 Combine like terms: -4 + 49 = 45 49 + 14a + a2 = 45 Factor a perfect square on the left side: (a + 7)(a + 7) = 45 Calculate the square root of the right side: 6.708203933 Break this problem into two subproblems by setting (a + 7) equal to 6.708203933 and -6.708203933.Subproblem 1
a + 7 = 6.708203933 Simplifying a + 7 = 6.708203933 Reorder the terms: 7 + a = 6.708203933 Solving 7 + a = 6.708203933 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + a = 6.708203933 + -7 Combine like terms: 7 + -7 = 0 0 + a = 6.708203933 + -7 a = 6.708203933 + -7 Combine like terms: 6.708203933 + -7 = -0.291796067 a = -0.291796067 Simplifying a = -0.291796067Subproblem 2
a + 7 = -6.708203933 Simplifying a + 7 = -6.708203933 Reorder the terms: 7 + a = -6.708203933 Solving 7 + a = -6.708203933 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + a = -6.708203933 + -7 Combine like terms: 7 + -7 = 0 0 + a = -6.708203933 + -7 a = -6.708203933 + -7 Combine like terms: -6.708203933 + -7 = -13.708203933 a = -13.708203933 Simplifying a = -13.708203933Solution
The solution to the problem is based on the solutions from the subproblems. a = {-0.291796067, -13.708203933}
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