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Simplifying 2n2 + 21 = -1n Reorder the terms: 21 + 2n2 = -1n Solving 21 + 2n2 = -1n Solving for variable 'n'. Reorder the terms: 21 + n + 2n2 = -1n + n Combine like terms: -1n + n = 0 21 + n + 2n2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 10.5 + 0.5n + n2 = 0 Move the constant term to the right: Add '-10.5' to each side of the equation. 10.5 + 0.5n + -10.5 + n2 = 0 + -10.5 Reorder the terms: 10.5 + -10.5 + 0.5n + n2 = 0 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + 0.5n + n2 = 0 + -10.5 0.5n + n2 = 0 + -10.5 Combine like terms: 0 + -10.5 = -10.5 0.5n + n2 = -10.5 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. 0.5n + 0.25 + n2 = -10.5 + 0.25 Reorder the terms: 0.25 + 0.5n + n2 = -10.5 + 0.25 Combine like terms: -10.5 + 0.25 = -10.25 0.25 + 0.5n + n2 = -10.25 Factor a perfect square on the left side: (n + 0.5)(n + 0.5) = -10.25 Can't calculate square root of the right side. The solution to this equation could not be determined.
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