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Simplifying -4n(n + -1) = 6.5 Reorder the terms: -4n(-1 + n) = 6.5 (-1 * -4n + n * -4n) = 6.5 (4n + -4n2) = 6.5 Solving 4n + -4n2 = 6.5 Solving for variable 'n'. Reorder the terms: -6.5 + 4n + -4n2 = 6.5 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 -6.5 + 4n + -4n2 = 0.0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. 1.625 + -1n + n2 = 0.0 Move the constant term to the right: Add '-1.625' to each side of the equation. 1.625 + -1n + -1.625 + n2 = 0.0 + -1.625 Reorder the terms: 1.625 + -1.625 + -1n + n2 = 0.0 + -1.625 Combine like terms: 1.625 + -1.625 = 0.000 0.000 + -1n + n2 = 0.0 + -1.625 -1n + n2 = 0.0 + -1.625 Combine like terms: 0.0 + -1.625 = -1.625 -1n + n2 = -1.625 The n term is -1n. 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 = -1.625 + 0.25 Reorder the terms: 0.25 + -1n + n2 = -1.625 + 0.25 Combine like terms: -1.625 + 0.25 = -1.375 0.25 + -1n + n2 = -1.375 Factor a perfect square on the left side: (n + -0.5)(n + -0.5) = -1.375 Can't calculate square root of the right side. The solution to this equation could not be determined.
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