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Simplifying a2 + 2a + 1 = 39 Reorder the terms: 1 + 2a + a2 = 39 Solving 1 + 2a + a2 = 39 Solving for variable 'a'. Reorder the terms: 1 + -39 + 2a + a2 = 39 + -39 Combine like terms: 1 + -39 = -38 -38 + 2a + a2 = 39 + -39 Combine like terms: 39 + -39 = 0 -38 + 2a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '38' to each side of the equation. -38 + 2a + 38 + a2 = 0 + 38 Reorder the terms: -38 + 38 + 2a + a2 = 0 + 38 Combine like terms: -38 + 38 = 0 0 + 2a + a2 = 0 + 38 2a + a2 = 0 + 38 Combine like terms: 0 + 38 = 38 2a + a2 = 38 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 = 38 + 1 Reorder the terms: 1 + 2a + a2 = 38 + 1 Combine like terms: 38 + 1 = 39 1 + 2a + a2 = 39 Factor a perfect square on the left side: (a + 1)(a + 1) = 39 Calculate the square root of the right side: 6.244997998 Break this problem into two subproblems by setting (a + 1) equal to 6.244997998 and -6.244997998.Subproblem 1
a + 1 = 6.244997998 Simplifying a + 1 = 6.244997998 Reorder the terms: 1 + a = 6.244997998 Solving 1 + a = 6.244997998 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 = 6.244997998 + -1 Combine like terms: 1 + -1 = 0 0 + a = 6.244997998 + -1 a = 6.244997998 + -1 Combine like terms: 6.244997998 + -1 = 5.244997998 a = 5.244997998 Simplifying a = 5.244997998Subproblem 2
a + 1 = -6.244997998 Simplifying a + 1 = -6.244997998 Reorder the terms: 1 + a = -6.244997998 Solving 1 + a = -6.244997998 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 = -6.244997998 + -1 Combine like terms: 1 + -1 = 0 0 + a = -6.244997998 + -1 a = -6.244997998 + -1 Combine like terms: -6.244997998 + -1 = -7.244997998 a = -7.244997998 Simplifying a = -7.244997998Solution
The solution to the problem is based on the solutions from the subproblems. a = {5.244997998, -7.244997998}
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