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Simplifying 5a2 + 27a + 42 = 0 Reorder the terms: 42 + 27a + 5a2 = 0 Solving 42 + 27a + 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'. 8.4 + 5.4a + a2 = 0 Move the constant term to the right: Add '-8.4' to each side of the equation. 8.4 + 5.4a + -8.4 + a2 = 0 + -8.4 Reorder the terms: 8.4 + -8.4 + 5.4a + a2 = 0 + -8.4 Combine like terms: 8.4 + -8.4 = 0.0 0.0 + 5.4a + a2 = 0 + -8.4 5.4a + a2 = 0 + -8.4 Combine like terms: 0 + -8.4 = -8.4 5.4a + a2 = -8.4 The a term is 5.4a. Take half its coefficient (2.7). Square it (7.29) and add it to both sides. Add '7.29' to each side of the equation. 5.4a + 7.29 + a2 = -8.4 + 7.29 Reorder the terms: 7.29 + 5.4a + a2 = -8.4 + 7.29 Combine like terms: -8.4 + 7.29 = -1.11 7.29 + 5.4a + a2 = -1.11 Factor a perfect square on the left side: (a + 2.7)(a + 2.7) = -1.11 Can't calculate square root of the right side. The solution to this equation could not be determined.
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