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Simplifying (a + -4)(a + -8) = -2 Reorder the terms: (-4 + a)(a + -8) = -2 Reorder the terms: (-4 + a)(-8 + a) = -2 Multiply (-4 + a) * (-8 + a) (-4(-8 + a) + a(-8 + a)) = -2 ((-8 * -4 + a * -4) + a(-8 + a)) = -2 ((32 + -4a) + a(-8 + a)) = -2 (32 + -4a + (-8 * a + a * a)) = -2 (32 + -4a + (-8a + a2)) = -2 Combine like terms: -4a + -8a = -12a (32 + -12a + a2) = -2 Solving 32 + -12a + a2 = -2 Solving for variable 'a'. Reorder the terms: 32 + 2 + -12a + a2 = -2 + 2 Combine like terms: 32 + 2 = 34 34 + -12a + a2 = -2 + 2 Combine like terms: -2 + 2 = 0 34 + -12a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '-34' to each side of the equation. 34 + -12a + -34 + a2 = 0 + -34 Reorder the terms: 34 + -34 + -12a + a2 = 0 + -34 Combine like terms: 34 + -34 = 0 0 + -12a + a2 = 0 + -34 -12a + a2 = 0 + -34 Combine like terms: 0 + -34 = -34 -12a + a2 = -34 The a term is -12a. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12a + 36 + a2 = -34 + 36 Reorder the terms: 36 + -12a + a2 = -34 + 36 Combine like terms: -34 + 36 = 2 36 + -12a + a2 = 2 Factor a perfect square on the left side: (a + -6)(a + -6) = 2 Calculate the square root of the right side: 1.414213562 Break this problem into two subproblems by setting (a + -6) equal to 1.414213562 and -1.414213562.Subproblem 1
a + -6 = 1.414213562 Simplifying a + -6 = 1.414213562 Reorder the terms: -6 + a = 1.414213562 Solving -6 + a = 1.414213562 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + a = 1.414213562 + 6 Combine like terms: -6 + 6 = 0 0 + a = 1.414213562 + 6 a = 1.414213562 + 6 Combine like terms: 1.414213562 + 6 = 7.414213562 a = 7.414213562 Simplifying a = 7.414213562Subproblem 2
a + -6 = -1.414213562 Simplifying a + -6 = -1.414213562 Reorder the terms: -6 + a = -1.414213562 Solving -6 + a = -1.414213562 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + a = -1.414213562 + 6 Combine like terms: -6 + 6 = 0 0 + a = -1.414213562 + 6 a = -1.414213562 + 6 Combine like terms: -1.414213562 + 6 = 4.585786438 a = 4.585786438 Simplifying a = 4.585786438Solution
The solution to the problem is based on the solutions from the subproblems. a = {7.414213562, 4.585786438}
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