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Simplifying 7(5a + 4b) + 4(5a + 2b) = 0 (5a * 7 + 4b * 7) + 4(5a + 2b) = 0 (35a + 28b) + 4(5a + 2b) = 0 35a + 28b + (5a * 4 + 2b * 4) = 0 35a + 28b + (20a + 8b) = 0 Reorder the terms: 35a + 20a + 28b + 8b = 0 Combine like terms: 35a + 20a = 55a 55a + 28b + 8b = 0 Combine like terms: 28b + 8b = 36b 55a + 36b = 0 Solving 55a + 36b = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-36b' to each side of the equation. 55a + 36b + -36b = 0 + -36b Combine like terms: 36b + -36b = 0 55a + 0 = 0 + -36b 55a = 0 + -36b Remove the zero: 55a = -36b Divide each side by '55'. a = -0.6545454545b Simplifying a = -0.6545454545b
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