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Simplifying a2 + 2a + 1 = 32 Reorder the terms: 1 + 2a + a2 = 32 Solving 1 + 2a + a2 = 32 Solving for variable 'a'. Reorder the terms: 1 + -32 + 2a + a2 = 32 + -32 Combine like terms: 1 + -32 = -31 -31 + 2a + a2 = 32 + -32 Combine like terms: 32 + -32 = 0 -31 + 2a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '31' to each side of the equation. -31 + 2a + 31 + a2 = 0 + 31 Reorder the terms: -31 + 31 + 2a + a2 = 0 + 31 Combine like terms: -31 + 31 = 0 0 + 2a + a2 = 0 + 31 2a + a2 = 0 + 31 Combine like terms: 0 + 31 = 31 2a + a2 = 31 The a term is 2a. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2a + 1 + a2 = 31 + 1 Reorder the terms: 1 + 2a + a2 = 31 + 1 Combine like terms: 31 + 1 = 32 1 + 2a + a2 = 32 Factor a perfect square on the left side: (a + 1)(a + 1) = 32 Calculate the square root of the right side: 5.656854249 Break this problem into two subproblems by setting (a + 1) equal to 5.656854249 and -5.656854249.Subproblem 1
a + 1 = 5.656854249 Simplifying a + 1 = 5.656854249 Reorder the terms: 1 + a = 5.656854249 Solving 1 + a = 5.656854249 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + a = 5.656854249 + -1 Combine like terms: 1 + -1 = 0 0 + a = 5.656854249 + -1 a = 5.656854249 + -1 Combine like terms: 5.656854249 + -1 = 4.656854249 a = 4.656854249 Simplifying a = 4.656854249Subproblem 2
a + 1 = -5.656854249 Simplifying a + 1 = -5.656854249 Reorder the terms: 1 + a = -5.656854249 Solving 1 + a = -5.656854249 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + a = -5.656854249 + -1 Combine like terms: 1 + -1 = 0 0 + a = -5.656854249 + -1 a = -5.656854249 + -1 Combine like terms: -5.656854249 + -1 = -6.656854249 a = -6.656854249 Simplifying a = -6.656854249Solution
The solution to the problem is based on the solutions from the subproblems. a = {4.656854249, -6.656854249}
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