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Simplifying 5n + -2n(2 + -1n) = -7 5n + (2 * -2n + -1n * -2n) = -7 5n + (-4n + 2n2) = -7 Combine like terms: 5n + -4n = 1n 1n + 2n2 = -7 Solving 1n + 2n2 = -7 Solving for variable 'n'. Reorder the terms: 7 + 1n + 2n2 = -7 + 7 Combine like terms: -7 + 7 = 0 7 + 1n + 2n2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 3.5 + 0.5n + n2 = 0 Move the constant term to the right: Add '-3.5' to each side of the equation. 3.5 + 0.5n + -3.5 + n2 = 0 + -3.5 Reorder the terms: 3.5 + -3.5 + 0.5n + n2 = 0 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + 0.5n + n2 = 0 + -3.5 0.5n + n2 = 0 + -3.5 Combine like terms: 0 + -3.5 = -3.5 0.5n + n2 = -3.5 The n term is 0.5n. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5n + 0.0625 + n2 = -3.5 + 0.0625 Reorder the terms: 0.0625 + 0.5n + n2 = -3.5 + 0.0625 Combine like terms: -3.5 + 0.0625 = -3.4375 0.0625 + 0.5n + n2 = -3.4375 Factor a perfect square on the left side: (n + 0.25)(n + 0.25) = -3.4375 Can't calculate square root of the right side. The solution to this equation could not be determined.
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