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Simplifying a2 + 2a + -40 = 0 Reorder the terms: -40 + 2a + a2 = 0 Solving -40 + 2a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '40' to each side of the equation. -40 + 2a + 40 + a2 = 0 + 40 Reorder the terms: -40 + 40 + 2a + a2 = 0 + 40 Combine like terms: -40 + 40 = 0 0 + 2a + a2 = 0 + 40 2a + a2 = 0 + 40 Combine like terms: 0 + 40 = 40 2a + a2 = 40 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 = 40 + 1 Reorder the terms: 1 + 2a + a2 = 40 + 1 Combine like terms: 40 + 1 = 41 1 + 2a + a2 = 41 Factor a perfect square on the left side: (a + 1)(a + 1) = 41 Calculate the square root of the right side: 6.403124237 Break this problem into two subproblems by setting (a + 1) equal to 6.403124237 and -6.403124237.Subproblem 1
a + 1 = 6.403124237 Simplifying a + 1 = 6.403124237 Reorder the terms: 1 + a = 6.403124237 Solving 1 + a = 6.403124237 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 = 6.403124237 + -1 Combine like terms: 1 + -1 = 0 0 + a = 6.403124237 + -1 a = 6.403124237 + -1 Combine like terms: 6.403124237 + -1 = 5.403124237 a = 5.403124237 Simplifying a = 5.403124237Subproblem 2
a + 1 = -6.403124237 Simplifying a + 1 = -6.403124237 Reorder the terms: 1 + a = -6.403124237 Solving 1 + a = -6.403124237 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 = -6.403124237 + -1 Combine like terms: 1 + -1 = 0 0 + a = -6.403124237 + -1 a = -6.403124237 + -1 Combine like terms: -6.403124237 + -1 = -7.403124237 a = -7.403124237 Simplifying a = -7.403124237Solution
The solution to the problem is based on the solutions from the subproblems. a = {5.403124237, -7.403124237}
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