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Simplifying 3n2 + 9n + 7 = 0 Reorder the terms: 7 + 9n + 3n2 = 0 Solving 7 + 9n + 3n2 = 0 Solving for variable 'n'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 2.333333333 + 3n + n2 = 0 Move the constant term to the right: Add '-2.333333333' to each side of the equation. 2.333333333 + 3n + -2.333333333 + n2 = 0 + -2.333333333 Reorder the terms: 2.333333333 + -2.333333333 + 3n + n2 = 0 + -2.333333333 Combine like terms: 2.333333333 + -2.333333333 = 0.000000000 0.000000000 + 3n + n2 = 0 + -2.333333333 3n + n2 = 0 + -2.333333333 Combine like terms: 0 + -2.333333333 = -2.333333333 3n + n2 = -2.333333333 The n term is 3n. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3n + 2.25 + n2 = -2.333333333 + 2.25 Reorder the terms: 2.25 + 3n + n2 = -2.333333333 + 2.25 Combine like terms: -2.333333333 + 2.25 = -0.083333333 2.25 + 3n + n2 = -0.083333333 Factor a perfect square on the left side: (n + 1.5)(n + 1.5) = -0.083333333 Can't calculate square root of the right side. The solution to this equation could not be determined.
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