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Simplifying (x + -7)(8a + -1b) + (x + 7)(8a + -1b) = 0 Reorder the terms: (-7 + x)(8a + -1b) + (x + 7)(8a + -1b) = 0 Multiply (-7 + x) * (8a + -1b) (-7(8a + -1b) + x(8a + -1b)) + (x + 7)(8a + -1b) = 0 ((8a * -7 + -1b * -7) + x(8a + -1b)) + (x + 7)(8a + -1b) = 0 ((-56a + 7b) + x(8a + -1b)) + (x + 7)(8a + -1b) = 0 (-56a + 7b + (8a * x + -1b * x)) + (x + 7)(8a + -1b) = 0 (-56a + 7b + (8ax + -1bx)) + (x + 7)(8a + -1b) = 0 Reorder the terms: (-56a + 8ax + 7b + -1bx) + (x + 7)(8a + -1b) = 0 (-56a + 8ax + 7b + -1bx) + (x + 7)(8a + -1b) = 0 Reorder the terms: -56a + 8ax + 7b + -1bx + (7 + x)(8a + -1b) = 0 Multiply (7 + x) * (8a + -1b) -56a + 8ax + 7b + -1bx + (7(8a + -1b) + x(8a + -1b)) = 0 -56a + 8ax + 7b + -1bx + ((8a * 7 + -1b * 7) + x(8a + -1b)) = 0 -56a + 8ax + 7b + -1bx + ((56a + -7b) + x(8a + -1b)) = 0 -56a + 8ax + 7b + -1bx + (56a + -7b + (8a * x + -1b * x)) = 0 -56a + 8ax + 7b + -1bx + (56a + -7b + (8ax + -1bx)) = 0 Reorder the terms: -56a + 8ax + 7b + -1bx + (56a + 8ax + -7b + -1bx) = 0 -56a + 8ax + 7b + -1bx + (56a + 8ax + -7b + -1bx) = 0 Reorder the terms: -56a + 56a + 8ax + 8ax + 7b + -7b + -1bx + -1bx = 0 Combine like terms: -56a + 56a = 0 0 + 8ax + 8ax + 7b + -7b + -1bx + -1bx = 0 8ax + 8ax + 7b + -7b + -1bx + -1bx = 0 Combine like terms: 8ax + 8ax = 16ax 16ax + 7b + -7b + -1bx + -1bx = 0 Combine like terms: 7b + -7b = 0 16ax + 0 + -1bx + -1bx = 0 16ax + -1bx + -1bx = 0 Combine like terms: -1bx + -1bx = -2bx 16ax + -2bx = 0 Solving 16ax + -2bx = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '2bx' to each side of the equation. 16ax + -2bx + 2bx = 0 + 2bx Combine like terms: -2bx + 2bx = 0 16ax + 0 = 0 + 2bx 16ax = 0 + 2bx Remove the zero: 16ax = 2bx Divide each side by '16x'. a = 0.125b Simplifying a = 0.125b
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