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Simplifying (a2 + a + 3) + (15a2 + 2a + 9) = 0 Reorder the terms: (3 + a + a2) + (15a2 + 2a + 9) = 0 Remove parenthesis around (3 + a + a2) 3 + a + a2 + (15a2 + 2a + 9) = 0 Reorder the terms: 3 + a + a2 + (9 + 2a + 15a2) = 0 Remove parenthesis around (9 + 2a + 15a2) 3 + a + a2 + 9 + 2a + 15a2 = 0 Reorder the terms: 3 + 9 + a + 2a + a2 + 15a2 = 0 Combine like terms: 3 + 9 = 12 12 + a + 2a + a2 + 15a2 = 0 Combine like terms: a + 2a = 3a 12 + 3a + a2 + 15a2 = 0 Combine like terms: a2 + 15a2 = 16a2 12 + 3a + 16a2 = 0 Solving 12 + 3a + 16a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 0.75 + 0.1875a + a2 = 0 Move the constant term to the right: Add '-0.75' to each side of the equation. 0.75 + 0.1875a + -0.75 + a2 = 0 + -0.75 Reorder the terms: 0.75 + -0.75 + 0.1875a + a2 = 0 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + 0.1875a + a2 = 0 + -0.75 0.1875a + a2 = 0 + -0.75 Combine like terms: 0 + -0.75 = -0.75 0.1875a + a2 = -0.75 The a term is 0.1875a. Take half its coefficient (0.09375). Square it (0.0087890625) and add it to both sides. Add '0.0087890625' to each side of the equation. 0.1875a + 0.0087890625 + a2 = -0.75 + 0.0087890625 Reorder the terms: 0.0087890625 + 0.1875a + a2 = -0.75 + 0.0087890625 Combine like terms: -0.75 + 0.0087890625 = -0.7412109375 0.0087890625 + 0.1875a + a2 = -0.7412109375 Factor a perfect square on the left side: (a + 0.09375)(a + 0.09375) = -0.7412109375 Can't calculate square root of the right side. The solution to this equation could not be determined.
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