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Simplifying a2 + 16a + 6 = 7 Reorder the terms: 6 + 16a + a2 = 7 Solving 6 + 16a + a2 = 7 Solving for variable 'a'. Reorder the terms: 6 + -7 + 16a + a2 = 7 + -7 Combine like terms: 6 + -7 = -1 -1 + 16a + a2 = 7 + -7 Combine like terms: 7 + -7 = 0 -1 + 16a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '1' to each side of the equation. -1 + 16a + 1 + a2 = 0 + 1 Reorder the terms: -1 + 1 + 16a + a2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 16a + a2 = 0 + 1 16a + a2 = 0 + 1 Combine like terms: 0 + 1 = 1 16a + a2 = 1 The a term is 16a. Take half its coefficient (8). Square it (64) and add it to both sides. Add '64' to each side of the equation. 16a + 64 + a2 = 1 + 64 Reorder the terms: 64 + 16a + a2 = 1 + 64 Combine like terms: 1 + 64 = 65 64 + 16a + a2 = 65 Factor a perfect square on the left side: (a + 8)(a + 8) = 65 Calculate the square root of the right side: 8.062257748 Break this problem into two subproblems by setting (a + 8) equal to 8.062257748 and -8.062257748.Subproblem 1
a + 8 = 8.062257748 Simplifying a + 8 = 8.062257748 Reorder the terms: 8 + a = 8.062257748 Solving 8 + a = 8.062257748 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + a = 8.062257748 + -8 Combine like terms: 8 + -8 = 0 0 + a = 8.062257748 + -8 a = 8.062257748 + -8 Combine like terms: 8.062257748 + -8 = 0.062257748 a = 0.062257748 Simplifying a = 0.062257748Subproblem 2
a + 8 = -8.062257748 Simplifying a + 8 = -8.062257748 Reorder the terms: 8 + a = -8.062257748 Solving 8 + a = -8.062257748 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + a = -8.062257748 + -8 Combine like terms: 8 + -8 = 0 0 + a = -8.062257748 + -8 a = -8.062257748 + -8 Combine like terms: -8.062257748 + -8 = -16.062257748 a = -16.062257748 Simplifying a = -16.062257748Solution
The solution to the problem is based on the solutions from the subproblems. a = {0.062257748, -16.062257748}
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