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Simplifying (a * 2) + (a + 4)(a + -1) = 14 Reorder the terms for easier multiplication: (2a) + (a + 4)(a + -1) = 14 Reorder the terms: (2a) + (4 + a)(a + -1) = 14 Reorder the terms: (2a) + (4 + a)(-1 + a) = 14 Multiply (4 + a) * (-1 + a) (2a) + (4(-1 + a) + a(-1 + a)) = 14 (2a) + ((-1 * 4 + a * 4) + a(-1 + a)) = 14 (2a) + ((-4 + 4a) + a(-1 + a)) = 14 (2a) + (-4 + 4a + (-1 * a + a * a)) = 14 (2a) + (-4 + 4a + (-1a + a2)) = 14 Combine like terms: 4a + -1a = 3a (2a) + (-4 + 3a + a2) = 14 Reorder the terms: -4 + (2a) + 3a + a2 = 14 Combine like terms: (2a) + 3a = 5a -4 + 5a + a2 = 14 Solving -4 + 5a + a2 = 14 Solving for variable 'a'. Reorder the terms: -4 + -14 + 5a + a2 = 14 + -14 Combine like terms: -4 + -14 = -18 -18 + 5a + a2 = 14 + -14 Combine like terms: 14 + -14 = 0 -18 + 5a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '18' to each side of the equation. -18 + 5a + 18 + a2 = 0 + 18 Reorder the terms: -18 + 18 + 5a + a2 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + 5a + a2 = 0 + 18 5a + a2 = 0 + 18 Combine like terms: 0 + 18 = 18 5a + a2 = 18 The a term is 5a. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5a + 6.25 + a2 = 18 + 6.25 Reorder the terms: 6.25 + 5a + a2 = 18 + 6.25 Combine like terms: 18 + 6.25 = 24.25 6.25 + 5a + a2 = 24.25 Factor a perfect square on the left side: (a + 2.5)(a + 2.5) = 24.25 Calculate the square root of the right side: 4.924428901 Break this problem into two subproblems by setting (a + 2.5) equal to 4.924428901 and -4.924428901.Subproblem 1
a + 2.5 = 4.924428901 Simplifying a + 2.5 = 4.924428901 Reorder the terms: 2.5 + a = 4.924428901 Solving 2.5 + a = 4.924428901 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + a = 4.924428901 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + a = 4.924428901 + -2.5 a = 4.924428901 + -2.5 Combine like terms: 4.924428901 + -2.5 = 2.424428901 a = 2.424428901 Simplifying a = 2.424428901Subproblem 2
a + 2.5 = -4.924428901 Simplifying a + 2.5 = -4.924428901 Reorder the terms: 2.5 + a = -4.924428901 Solving 2.5 + a = -4.924428901 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + a = -4.924428901 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + a = -4.924428901 + -2.5 a = -4.924428901 + -2.5 Combine like terms: -4.924428901 + -2.5 = -7.424428901 a = -7.424428901 Simplifying a = -7.424428901Solution
The solution to the problem is based on the solutions from the subproblems. a = {2.424428901, -7.424428901}
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