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Simplifying 12n2 + n + 9 = 0 Reorder the terms: 9 + n + 12n2 = 0 Solving 9 + n + 12n2 = 0 Solving for variable 'n'. Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. 0.75 + 0.08333333333n + n2 = 0 Move the constant term to the right: Add '-0.75' to each side of the equation. 0.75 + 0.08333333333n + -0.75 + n2 = 0 + -0.75 Reorder the terms: 0.75 + -0.75 + 0.08333333333n + n2 = 0 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + 0.08333333333n + n2 = 0 + -0.75 0.08333333333n + n2 = 0 + -0.75 Combine like terms: 0 + -0.75 = -0.75 0.08333333333n + n2 = -0.75 The n term is n. 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. 0.08333333333n + 0.25 + n2 = -0.75 + 0.25 Reorder the terms: 0.25 + 0.08333333333n + n2 = -0.75 + 0.25 Combine like terms: -0.75 + 0.25 = -0.5 0.25 + 0.08333333333n + n2 = -0.5 Factor a perfect square on the left side: (n + 0.5)(n + 0.5) = -0.5 Can't calculate square root of the right side. The solution to this equation could not be determined.
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