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Simplifying 4n2 + 2n + 3 = 0 Reorder the terms: 3 + 2n + 4n2 = 0 Solving 3 + 2n + 4n2 = 0 Solving for variable 'n'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 0.75 + 0.5n + n2 = 0 Move the constant term to the right: Add '-0.75' to each side of the equation. 0.75 + 0.5n + -0.75 + n2 = 0 + -0.75 Reorder the terms: 0.75 + -0.75 + 0.5n + n2 = 0 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + 0.5n + n2 = 0 + -0.75 0.5n + n2 = 0 + -0.75 Combine like terms: 0 + -0.75 = -0.75 0.5n + n2 = -0.75 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 = -0.75 + 0.0625 Reorder the terms: 0.0625 + 0.5n + n2 = -0.75 + 0.0625 Combine like terms: -0.75 + 0.0625 = -0.6875 0.0625 + 0.5n + n2 = -0.6875 Factor a perfect square on the left side: (n + 0.25)(n + 0.25) = -0.6875 Can't calculate square root of the right side. The solution to this equation could not be determined.
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