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Simplifying a2 + 13a + -3 = 0 Reorder the terms: -3 + 13a + a2 = 0 Solving -3 + 13a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '3' to each side of the equation. -3 + 13a + 3 + a2 = 0 + 3 Reorder the terms: -3 + 3 + 13a + a2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 13a + a2 = 0 + 3 13a + a2 = 0 + 3 Combine like terms: 0 + 3 = 3 13a + a2 = 3 The a term is 13a. Take half its coefficient (6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. 13a + 42.25 + a2 = 3 + 42.25 Reorder the terms: 42.25 + 13a + a2 = 3 + 42.25 Combine like terms: 3 + 42.25 = 45.25 42.25 + 13a + a2 = 45.25 Factor a perfect square on the left side: (a + 6.5)(a + 6.5) = 45.25 Calculate the square root of the right side: 6.726812024 Break this problem into two subproblems by setting (a + 6.5) equal to 6.726812024 and -6.726812024.Subproblem 1
a + 6.5 = 6.726812024 Simplifying a + 6.5 = 6.726812024 Reorder the terms: 6.5 + a = 6.726812024 Solving 6.5 + a = 6.726812024 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + a = 6.726812024 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + a = 6.726812024 + -6.5 a = 6.726812024 + -6.5 Combine like terms: 6.726812024 + -6.5 = 0.226812024 a = 0.226812024 Simplifying a = 0.226812024Subproblem 2
a + 6.5 = -6.726812024 Simplifying a + 6.5 = -6.726812024 Reorder the terms: 6.5 + a = -6.726812024 Solving 6.5 + a = -6.726812024 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + a = -6.726812024 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + a = -6.726812024 + -6.5 a = -6.726812024 + -6.5 Combine like terms: -6.726812024 + -6.5 = -13.226812024 a = -13.226812024 Simplifying a = -13.226812024Solution
The solution to the problem is based on the solutions from the subproblems. a = {0.226812024, -13.226812024}
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