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Simplifying 32n2 = -12n + -7 Reorder the terms: 32n2 = -7 + -12n Solving 32n2 = -7 + -12n Solving for variable 'n'. Reorder the terms: 7 + 12n + 32n2 = -7 + -12n + 7 + 12n Reorder the terms: 7 + 12n + 32n2 = -7 + 7 + -12n + 12n Combine like terms: -7 + 7 = 0 7 + 12n + 32n2 = 0 + -12n + 12n 7 + 12n + 32n2 = -12n + 12n Combine like terms: -12n + 12n = 0 7 + 12n + 32n2 = 0 Begin completing the square. Divide all terms by 32 the coefficient of the squared term: Divide each side by '32'. 0.21875 + 0.375n + n2 = 0 Move the constant term to the right: Add '-0.21875' to each side of the equation. 0.21875 + 0.375n + -0.21875 + n2 = 0 + -0.21875 Reorder the terms: 0.21875 + -0.21875 + 0.375n + n2 = 0 + -0.21875 Combine like terms: 0.21875 + -0.21875 = 0.00000 0.00000 + 0.375n + n2 = 0 + -0.21875 0.375n + n2 = 0 + -0.21875 Combine like terms: 0 + -0.21875 = -0.21875 0.375n + n2 = -0.21875 The n term is 0.375n. Take half its coefficient (0.1875). Square it (0.03515625) and add it to both sides. Add '0.03515625' to each side of the equation. 0.375n + 0.03515625 + n2 = -0.21875 + 0.03515625 Reorder the terms: 0.03515625 + 0.375n + n2 = -0.21875 + 0.03515625 Combine like terms: -0.21875 + 0.03515625 = -0.18359375 0.03515625 + 0.375n + n2 = -0.18359375 Factor a perfect square on the left side: (n + 0.1875)(n + 0.1875) = -0.18359375 Can't calculate square root of the right side. The solution to this equation could not be determined.
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