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Simplifying 2 = n2 + -1n + 12 Reorder the terms: 2 = 12 + -1n + n2 Solving 2 = 12 + -1n + n2 Solving for variable 'n'. Combine like terms: 2 + -12 = -10 -10 + n + -1n2 = 12 + -1n + n2 + -12 + n + -1n2 Reorder the terms: -10 + n + -1n2 = 12 + -12 + -1n + n + n2 + -1n2 Combine like terms: 12 + -12 = 0 -10 + n + -1n2 = 0 + -1n + n + n2 + -1n2 -10 + n + -1n2 = -1n + n + n2 + -1n2 Combine like terms: -1n + n = 0 -10 + n + -1n2 = 0 + n2 + -1n2 -10 + n + -1n2 = n2 + -1n2 Combine like terms: n2 + -1n2 = 0 -10 + n + -1n2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 10 + -1n + n2 = 0 Move the constant term to the right: Add '-10' to each side of the equation. 10 + -1n + -10 + n2 = 0 + -10 Reorder the terms: 10 + -10 + -1n + n2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -1n + n2 = 0 + -10 -1n + n2 = 0 + -10 Combine like terms: 0 + -10 = -10 -1n + n2 = -10 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. -1n + 0.25 + n2 = -10 + 0.25 Reorder the terms: 0.25 + -1n + n2 = -10 + 0.25 Combine like terms: -10 + 0.25 = -9.75 0.25 + -1n + n2 = -9.75 Factor a perfect square on the left side: (n + 0.5)(n + 0.5) = -9.75 Can't calculate square root of the right side. The solution to this equation could not be determined.
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