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Simplifying 5(2a + 4b) + 7(5a + 2b) = 0 (2a * 5 + 4b * 5) + 7(5a + 2b) = 0 (10a + 20b) + 7(5a + 2b) = 0 10a + 20b + (5a * 7 + 2b * 7) = 0 10a + 20b + (35a + 14b) = 0 Reorder the terms: 10a + 35a + 20b + 14b = 0 Combine like terms: 10a + 35a = 45a 45a + 20b + 14b = 0 Combine like terms: 20b + 14b = 34b 45a + 34b = 0 Solving 45a + 34b = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-34b' to each side of the equation. 45a + 34b + -34b = 0 + -34b Combine like terms: 34b + -34b = 0 45a + 0 = 0 + -34b 45a = 0 + -34b Remove the zero: 45a = -34b Divide each side by '45'. a = -0.7555555556b Simplifying a = -0.7555555556b
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