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Simplifying 2n2 + 12n + 36 = -7 Reorder the terms: 36 + 12n + 2n2 = -7 Solving 36 + 12n + 2n2 = -7 Solving for variable 'n'. Reorder the terms: 36 + 7 + 12n + 2n2 = -7 + 7 Combine like terms: 36 + 7 = 43 43 + 12n + 2n2 = -7 + 7 Combine like terms: -7 + 7 = 0 43 + 12n + 2n2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 21.5 + 6n + n2 = 0 Move the constant term to the right: Add '-21.5' to each side of the equation. 21.5 + 6n + -21.5 + n2 = 0 + -21.5 Reorder the terms: 21.5 + -21.5 + 6n + n2 = 0 + -21.5 Combine like terms: 21.5 + -21.5 = 0.0 0.0 + 6n + n2 = 0 + -21.5 6n + n2 = 0 + -21.5 Combine like terms: 0 + -21.5 = -21.5 6n + n2 = -21.5 The n term is 6n. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6n + 9 + n2 = -21.5 + 9 Reorder the terms: 9 + 6n + n2 = -21.5 + 9 Combine like terms: -21.5 + 9 = -12.5 9 + 6n + n2 = -12.5 Factor a perfect square on the left side: (n + 3)(n + 3) = -12.5 Can't calculate square root of the right side. The solution to this equation could not be determined.
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