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Simplifying 11(-4a + 3b + -4c) + -9(3a + -6b + 2c) = 0 (-4a * 11 + 3b * 11 + -4c * 11) + -9(3a + -6b + 2c) = 0 (-44a + 33b + -44c) + -9(3a + -6b + 2c) = 0 -44a + 33b + -44c + (3a * -9 + -6b * -9 + 2c * -9) = 0 -44a + 33b + -44c + (-27a + 54b + -18c) = 0 Reorder the terms: -44a + -27a + 33b + 54b + -44c + -18c = 0 Combine like terms: -44a + -27a = -71a -71a + 33b + 54b + -44c + -18c = 0 Combine like terms: 33b + 54b = 87b -71a + 87b + -44c + -18c = 0 Combine like terms: -44c + -18c = -62c -71a + 87b + -62c = 0 Solving -71a + 87b + -62c = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-87b' to each side of the equation. -71a + 87b + -87b + -62c = 0 + -87b Combine like terms: 87b + -87b = 0 -71a + 0 + -62c = 0 + -87b -71a + -62c = 0 + -87b Remove the zero: -71a + -62c = -87b Add '62c' to each side of the equation. -71a + -62c + 62c = -87b + 62c Combine like terms: -62c + 62c = 0 -71a + 0 = -87b + 62c -71a = -87b + 62c Divide each side by '-71'. a = 1.225352113b + -0.8732394366c Simplifying a = 1.225352113b + -0.8732394366c
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