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Simplifying (a + -1)(a + 2) = 14 Reorder the terms: (-1 + a)(a + 2) = 14 Reorder the terms: (-1 + a)(2 + a) = 14 Multiply (-1 + a) * (2 + a) (-1(2 + a) + a(2 + a)) = 14 ((2 * -1 + a * -1) + a(2 + a)) = 14 ((-2 + -1a) + a(2 + a)) = 14 (-2 + -1a + (2 * a + a * a)) = 14 (-2 + -1a + (2a + a2)) = 14 Combine like terms: -1a + 2a = 1a (-2 + 1a + a2) = 14 Solving -2 + 1a + a2 = 14 Solving for variable 'a'. Reorder the terms: -2 + -14 + 1a + a2 = 14 + -14 Combine like terms: -2 + -14 = -16 -16 + 1a + a2 = 14 + -14 Combine like terms: 14 + -14 = 0 -16 + 1a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '16' to each side of the equation. -16 + 1a + 16 + a2 = 0 + 16 Reorder the terms: -16 + 16 + 1a + a2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + 1a + a2 = 0 + 16 1a + a2 = 0 + 16 Combine like terms: 0 + 16 = 16 1a + a2 = 16 The a term is 1a. 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 = 16 + 0.25 Reorder the terms: 0.25 + a + a2 = 16 + 0.25 Combine like terms: 16 + 0.25 = 16.25 0.25 + a + a2 = 16.25 Factor a perfect square on the left side: (a + 0.5)(a + 0.5) = 16.25 Calculate the square root of the right side: 4.031128874 Break this problem into two subproblems by setting (a + 0.5) equal to 4.031128874 and -4.031128874.Subproblem 1
a + 0.5 = 4.031128874 Simplifying a + 0.5 = 4.031128874 Reorder the terms: 0.5 + a = 4.031128874 Solving 0.5 + a = 4.031128874 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 = 4.031128874 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + a = 4.031128874 + -0.5 a = 4.031128874 + -0.5 Combine like terms: 4.031128874 + -0.5 = 3.531128874 a = 3.531128874 Simplifying a = 3.531128874Subproblem 2
a + 0.5 = -4.031128874 Simplifying a + 0.5 = -4.031128874 Reorder the terms: 0.5 + a = -4.031128874 Solving 0.5 + a = -4.031128874 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 = -4.031128874 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + a = -4.031128874 + -0.5 a = -4.031128874 + -0.5 Combine like terms: -4.031128874 + -0.5 = -4.531128874 a = -4.531128874 Simplifying a = -4.531128874Solution
The solution to the problem is based on the solutions from the subproblems. a = {3.531128874, -4.531128874}
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