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Simplifying a2 + 9a + -1 = 0 Reorder the terms: -1 + 9a + a2 = 0 Solving -1 + 9a + 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 + 9a + 1 + a2 = 0 + 1 Reorder the terms: -1 + 1 + 9a + a2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 9a + a2 = 0 + 1 9a + a2 = 0 + 1 Combine like terms: 0 + 1 = 1 9a + a2 = 1 The a term is 9a. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9a + 20.25 + a2 = 1 + 20.25 Reorder the terms: 20.25 + 9a + a2 = 1 + 20.25 Combine like terms: 1 + 20.25 = 21.25 20.25 + 9a + a2 = 21.25 Factor a perfect square on the left side: (a + 4.5)(a + 4.5) = 21.25 Calculate the square root of the right side: 4.609772229 Break this problem into two subproblems by setting (a + 4.5) equal to 4.609772229 and -4.609772229.Subproblem 1
a + 4.5 = 4.609772229 Simplifying a + 4.5 = 4.609772229 Reorder the terms: 4.5 + a = 4.609772229 Solving 4.5 + a = 4.609772229 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + a = 4.609772229 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + a = 4.609772229 + -4.5 a = 4.609772229 + -4.5 Combine like terms: 4.609772229 + -4.5 = 0.109772229 a = 0.109772229 Simplifying a = 0.109772229Subproblem 2
a + 4.5 = -4.609772229 Simplifying a + 4.5 = -4.609772229 Reorder the terms: 4.5 + a = -4.609772229 Solving 4.5 + a = -4.609772229 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + a = -4.609772229 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + a = -4.609772229 + -4.5 a = -4.609772229 + -4.5 Combine like terms: -4.609772229 + -4.5 = -9.109772229 a = -9.109772229 Simplifying a = -9.109772229Solution
The solution to the problem is based on the solutions from the subproblems. a = {0.109772229, -9.109772229}
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