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Simplifying 4n2 = 3n + -7 Reorder the terms: 4n2 = -7 + 3n Solving 4n2 = -7 + 3n Solving for variable 'n'. Reorder the terms: 7 + -3n + 4n2 = -7 + 3n + 7 + -3n Reorder the terms: 7 + -3n + 4n2 = -7 + 7 + 3n + -3n Combine like terms: -7 + 7 = 0 7 + -3n + 4n2 = 0 + 3n + -3n 7 + -3n + 4n2 = 3n + -3n Combine like terms: 3n + -3n = 0 7 + -3n + 4n2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 1.75 + -0.75n + n2 = 0 Move the constant term to the right: Add '-1.75' to each side of the equation. 1.75 + -0.75n + -1.75 + n2 = 0 + -1.75 Reorder the terms: 1.75 + -1.75 + -0.75n + n2 = 0 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + -0.75n + n2 = 0 + -1.75 -0.75n + n2 = 0 + -1.75 Combine like terms: 0 + -1.75 = -1.75 -0.75n + n2 = -1.75 The n term is -0.75n. Take half its coefficient (-0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. -0.75n + 0.140625 + n2 = -1.75 + 0.140625 Reorder the terms: 0.140625 + -0.75n + n2 = -1.75 + 0.140625 Combine like terms: -1.75 + 0.140625 = -1.609375 0.140625 + -0.75n + n2 = -1.609375 Factor a perfect square on the left side: (n + -0.375)(n + -0.375) = -1.609375 Can't calculate square root of the right side. The solution to this equation could not be determined.
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