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Simplifying 5(8a + -1b) + -7(6b + -6a) = 0 (8a * 5 + -1b * 5) + -7(6b + -6a) = 0 (40a + -5b) + -7(6b + -6a) = 0 Reorder the terms: 40a + -5b + -7(-6a + 6b) = 0 40a + -5b + (-6a * -7 + 6b * -7) = 0 40a + -5b + (42a + -42b) = 0 Reorder the terms: 40a + 42a + -5b + -42b = 0 Combine like terms: 40a + 42a = 82a 82a + -5b + -42b = 0 Combine like terms: -5b + -42b = -47b 82a + -47b = 0 Solving 82a + -47b = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '47b' to each side of the equation. 82a + -47b + 47b = 0 + 47b Combine like terms: -47b + 47b = 0 82a + 0 = 0 + 47b 82a = 0 + 47b Remove the zero: 82a = 47b Divide each side by '82'. a = 0.5731707317b Simplifying a = 0.5731707317b
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