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Simplifying 5a2 + 3a + 12 = 0 Reorder the terms: 12 + 3a + 5a2 = 0 Solving 12 + 3a + 5a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 2.4 + 0.6a + a2 = 0 Move the constant term to the right: Add '-2.4' to each side of the equation. 2.4 + 0.6a + -2.4 + a2 = 0 + -2.4 Reorder the terms: 2.4 + -2.4 + 0.6a + a2 = 0 + -2.4 Combine like terms: 2.4 + -2.4 = 0.0 0.0 + 0.6a + a2 = 0 + -2.4 0.6a + a2 = 0 + -2.4 Combine like terms: 0 + -2.4 = -2.4 0.6a + a2 = -2.4 The a term is 0.6a. Take half its coefficient (0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. 0.6a + 0.09 + a2 = -2.4 + 0.09 Reorder the terms: 0.09 + 0.6a + a2 = -2.4 + 0.09 Combine like terms: -2.4 + 0.09 = -2.31 0.09 + 0.6a + a2 = -2.31 Factor a perfect square on the left side: (a + 0.3)(a + 0.3) = -2.31 Can't calculate square root of the right side. The solution to this equation could not be determined.
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