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Simplifying a2 + a + -41 = 0 Reorder the terms: -41 + a + a2 = 0 Solving -41 + a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '41' to each side of the equation. -41 + a + 41 + a2 = 0 + 41 Reorder the terms: -41 + 41 + a + a2 = 0 + 41 Combine like terms: -41 + 41 = 0 0 + a + a2 = 0 + 41 a + a2 = 0 + 41 Combine like terms: 0 + 41 = 41 a + a2 = 41 The a term is a. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. a + 0.25 + a2 = 41 + 0.25 Reorder the terms: 0.25 + a + a2 = 41 + 0.25 Combine like terms: 41 + 0.25 = 41.25 0.25 + a + a2 = 41.25 Factor a perfect square on the left side: (a + 0.5)(a + 0.5) = 41.25 Calculate the square root of the right side: 6.422616289 Break this problem into two subproblems by setting (a + 0.5) equal to 6.422616289 and -6.422616289.Subproblem 1
a + 0.5 = 6.422616289 Simplifying a + 0.5 = 6.422616289 Reorder the terms: 0.5 + a = 6.422616289 Solving 0.5 + a = 6.422616289 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + a = 6.422616289 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + a = 6.422616289 + -0.5 a = 6.422616289 + -0.5 Combine like terms: 6.422616289 + -0.5 = 5.922616289 a = 5.922616289 Simplifying a = 5.922616289Subproblem 2
a + 0.5 = -6.422616289 Simplifying a + 0.5 = -6.422616289 Reorder the terms: 0.5 + a = -6.422616289 Solving 0.5 + a = -6.422616289 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + a = -6.422616289 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + a = -6.422616289 + -0.5 a = -6.422616289 + -0.5 Combine like terms: -6.422616289 + -0.5 = -6.922616289 a = -6.922616289 Simplifying a = -6.922616289Solution
The solution to the problem is based on the solutions from the subproblems. a = {5.922616289, -6.922616289}
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