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Simplifying a2 + 3a + a2 + -6a + 35 = a2 + -5a + a2 + 7a Reorder the terms: 35 + 3a + -6a + a2 + a2 = a2 + -5a + a2 + 7a Combine like terms: 3a + -6a = -3a 35 + -3a + a2 + a2 = a2 + -5a + a2 + 7a Combine like terms: a2 + a2 = 2a2 35 + -3a + 2a2 = a2 + -5a + a2 + 7a Reorder the terms: 35 + -3a + 2a2 = -5a + 7a + a2 + a2 Combine like terms: -5a + 7a = 2a 35 + -3a + 2a2 = 2a + a2 + a2 Combine like terms: a2 + a2 = 2a2 35 + -3a + 2a2 = 2a + 2a2 Add '-2a2' to each side of the equation. 35 + -3a + 2a2 + -2a2 = 2a + 2a2 + -2a2 Combine like terms: 2a2 + -2a2 = 0 35 + -3a + 0 = 2a + 2a2 + -2a2 35 + -3a = 2a + 2a2 + -2a2 Combine like terms: 2a2 + -2a2 = 0 35 + -3a = 2a + 0 35 + -3a = 2a Solving 35 + -3a = 2a Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-2a' to each side of the equation. 35 + -3a + -2a = 2a + -2a Combine like terms: -3a + -2a = -5a 35 + -5a = 2a + -2a Combine like terms: 2a + -2a = 0 35 + -5a = 0 Add '-35' to each side of the equation. 35 + -35 + -5a = 0 + -35 Combine like terms: 35 + -35 = 0 0 + -5a = 0 + -35 -5a = 0 + -35 Combine like terms: 0 + -35 = -35 -5a = -35 Divide each side by '-5'. a = 7 Simplifying a = 7
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