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Simplifying a2 + 4.1a + 4 = 0 Reorder the terms: 4 + 4.1a + a2 = 0 Solving 4 + 4.1a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '-4' to each side of the equation. 4 + 4.1a + -4 + a2 = 0 + -4 Reorder the terms: 4 + -4 + 4.1a + a2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 4.1a + a2 = 0 + -4 4.1a + a2 = 0 + -4 Combine like terms: 0 + -4 = -4 4.1a + a2 = -4 The a term is 4.1a. Take half its coefficient (2.05). Square it (4.2025) and add it to both sides. Add '4.2025' to each side of the equation. 4.1a + 4.2025 + a2 = -4 + 4.2025 Reorder the terms: 4.2025 + 4.1a + a2 = -4 + 4.2025 Combine like terms: -4 + 4.2025 = 0.2025 4.2025 + 4.1a + a2 = 0.2025 Factor a perfect square on the left side: (a + 2.05)(a + 2.05) = 0.2025 Calculate the square root of the right side: 0.45 Break this problem into two subproblems by setting (a + 2.05) equal to 0.45 and -0.45.Subproblem 1
a + 2.05 = 0.45 Simplifying a + 2.05 = 0.45 Reorder the terms: 2.05 + a = 0.45 Solving 2.05 + a = 0.45 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-2.05' to each side of the equation. 2.05 + -2.05 + a = 0.45 + -2.05 Combine like terms: 2.05 + -2.05 = 0.00 0.00 + a = 0.45 + -2.05 a = 0.45 + -2.05 Combine like terms: 0.45 + -2.05 = -1.6 a = -1.6 Simplifying a = -1.6Subproblem 2
a + 2.05 = -0.45 Simplifying a + 2.05 = -0.45 Reorder the terms: 2.05 + a = -0.45 Solving 2.05 + a = -0.45 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-2.05' to each side of the equation. 2.05 + -2.05 + a = -0.45 + -2.05 Combine like terms: 2.05 + -2.05 = 0.00 0.00 + a = -0.45 + -2.05 a = -0.45 + -2.05 Combine like terms: -0.45 + -2.05 = -2.5 a = -2.5 Simplifying a = -2.5Solution
The solution to the problem is based on the solutions from the subproblems. a = {-1.6, -2.5}
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