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Simplifying a2 + 7a + 1 = 0 Reorder the terms: 1 + 7a + a2 = 0 Solving 1 + 7a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + 7a + -1 + a2 = 0 + -1 Reorder the terms: 1 + -1 + 7a + a2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 7a + a2 = 0 + -1 7a + a2 = 0 + -1 Combine like terms: 0 + -1 = -1 7a + a2 = -1 The a term is 7a. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7a + 12.25 + a2 = -1 + 12.25 Reorder the terms: 12.25 + 7a + a2 = -1 + 12.25 Combine like terms: -1 + 12.25 = 11.25 12.25 + 7a + a2 = 11.25 Factor a perfect square on the left side: (a + 3.5)(a + 3.5) = 11.25 Calculate the square root of the right side: 3.354101966 Break this problem into two subproblems by setting (a + 3.5) equal to 3.354101966 and -3.354101966.Subproblem 1
a + 3.5 = 3.354101966 Simplifying a + 3.5 = 3.354101966 Reorder the terms: 3.5 + a = 3.354101966 Solving 3.5 + a = 3.354101966 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + a = 3.354101966 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + a = 3.354101966 + -3.5 a = 3.354101966 + -3.5 Combine like terms: 3.354101966 + -3.5 = -0.145898034 a = -0.145898034 Simplifying a = -0.145898034Subproblem 2
a + 3.5 = -3.354101966 Simplifying a + 3.5 = -3.354101966 Reorder the terms: 3.5 + a = -3.354101966 Solving 3.5 + a = -3.354101966 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + a = -3.354101966 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + a = -3.354101966 + -3.5 a = -3.354101966 + -3.5 Combine like terms: -3.354101966 + -3.5 = -6.854101966 a = -6.854101966 Simplifying a = -6.854101966Solution
The solution to the problem is based on the solutions from the subproblems. a = {-0.145898034, -6.854101966}
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