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Simplifying 4n2 + 5n + 10 = 7 Reorder the terms: 10 + 5n + 4n2 = 7 Solving 10 + 5n + 4n2 = 7 Solving for variable 'n'. Reorder the terms: 10 + -7 + 5n + 4n2 = 7 + -7 Combine like terms: 10 + -7 = 3 3 + 5n + 4n2 = 7 + -7 Combine like terms: 7 + -7 = 0 3 + 5n + 4n2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 0.75 + 1.25n + n2 = 0 Move the constant term to the right: Add '-0.75' to each side of the equation. 0.75 + 1.25n + -0.75 + n2 = 0 + -0.75 Reorder the terms: 0.75 + -0.75 + 1.25n + n2 = 0 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + 1.25n + n2 = 0 + -0.75 1.25n + n2 = 0 + -0.75 Combine like terms: 0 + -0.75 = -0.75 1.25n + n2 = -0.75 The n term is 1.25n. Take half its coefficient (0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. 1.25n + 0.390625 + n2 = -0.75 + 0.390625 Reorder the terms: 0.390625 + 1.25n + n2 = -0.75 + 0.390625 Combine like terms: -0.75 + 0.390625 = -0.359375 0.390625 + 1.25n + n2 = -0.359375 Factor a perfect square on the left side: (n + 0.625)(n + 0.625) = -0.359375 Can't calculate square root of the right side. The solution to this equation could not be determined.
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