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Simplifying 4n + -5 = n2 + 3 Reorder the terms: -5 + 4n = n2 + 3 Reorder the terms: -5 + 4n = 3 + n2 Solving -5 + 4n = 3 + n2 Solving for variable 'n'. Reorder the terms: -5 + -3 + 4n + -1n2 = 3 + n2 + -3 + -1n2 Combine like terms: -5 + -3 = -8 -8 + 4n + -1n2 = 3 + n2 + -3 + -1n2 Reorder the terms: -8 + 4n + -1n2 = 3 + -3 + n2 + -1n2 Combine like terms: 3 + -3 = 0 -8 + 4n + -1n2 = 0 + n2 + -1n2 -8 + 4n + -1n2 = n2 + -1n2 Combine like terms: n2 + -1n2 = 0 -8 + 4n + -1n2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 8 + -4n + n2 = 0 Move the constant term to the right: Add '-8' to each side of the equation. 8 + -4n + -8 + n2 = 0 + -8 Reorder the terms: 8 + -8 + -4n + n2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -4n + n2 = 0 + -8 -4n + n2 = 0 + -8 Combine like terms: 0 + -8 = -8 -4n + n2 = -8 The n term is -4n. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4n + 4 + n2 = -8 + 4 Reorder the terms: 4 + -4n + n2 = -8 + 4 Combine like terms: -8 + 4 = -4 4 + -4n + n2 = -4 Factor a perfect square on the left side: (n + -2)(n + -2) = -4 Can't calculate square root of the right side. The solution to this equation could not be determined.
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