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Simplifying 4a2 + a + 9 = 0 Reorder the terms: 9 + a + 4a2 = 0 Solving 9 + a + 4a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 2.25 + 0.25a + a2 = 0 Move the constant term to the right: Add '-2.25' to each side of the equation. 2.25 + 0.25a + -2.25 + a2 = 0 + -2.25 Reorder the terms: 2.25 + -2.25 + 0.25a + a2 = 0 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + 0.25a + a2 = 0 + -2.25 0.25a + a2 = 0 + -2.25 Combine like terms: 0 + -2.25 = -2.25 0.25a + a2 = -2.25 The a term is a. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.25a + 0.25 + a2 = -2.25 + 0.25 Reorder the terms: 0.25 + 0.25a + a2 = -2.25 + 0.25 Combine like terms: -2.25 + 0.25 = -2 0.25 + 0.25a + a2 = -2 Factor a perfect square on the left side: (a + 0.5)(a + 0.5) = -2 Can't calculate square root of the right side. The solution to this equation could not be determined.
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