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Simplifying a2 + 7a + -8 = 8 Reorder the terms: -8 + 7a + a2 = 8 Solving -8 + 7a + a2 = 8 Solving for variable 'a'. Reorder the terms: -8 + -8 + 7a + a2 = 8 + -8 Combine like terms: -8 + -8 = -16 -16 + 7a + a2 = 8 + -8 Combine like terms: 8 + -8 = 0 -16 + 7a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '16' to each side of the equation. -16 + 7a + 16 + a2 = 0 + 16 Reorder the terms: -16 + 16 + 7a + a2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + 7a + a2 = 0 + 16 7a + a2 = 0 + 16 Combine like terms: 0 + 16 = 16 7a + a2 = 16 The a term is 7a. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7a + 12.25 + a2 = 16 + 12.25 Reorder the terms: 12.25 + 7a + a2 = 16 + 12.25 Combine like terms: 16 + 12.25 = 28.25 12.25 + 7a + a2 = 28.25 Factor a perfect square on the left side: (a + 3.5)(a + 3.5) = 28.25 Calculate the square root of the right side: 5.315072906 Break this problem into two subproblems by setting (a + 3.5) equal to 5.315072906 and -5.315072906.Subproblem 1
a + 3.5 = 5.315072906 Simplifying a + 3.5 = 5.315072906 Reorder the terms: 3.5 + a = 5.315072906 Solving 3.5 + a = 5.315072906 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + a = 5.315072906 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + a = 5.315072906 + -3.5 a = 5.315072906 + -3.5 Combine like terms: 5.315072906 + -3.5 = 1.815072906 a = 1.815072906 Simplifying a = 1.815072906Subproblem 2
a + 3.5 = -5.315072906 Simplifying a + 3.5 = -5.315072906 Reorder the terms: 3.5 + a = -5.315072906 Solving 3.5 + a = -5.315072906 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + a = -5.315072906 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + a = -5.315072906 + -3.5 a = -5.315072906 + -3.5 Combine like terms: -5.315072906 + -3.5 = -8.815072906 a = -8.815072906 Simplifying a = -8.815072906Solution
The solution to the problem is based on the solutions from the subproblems. a = {1.815072906, -8.815072906}
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