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Simplifying 3n2 = -12 + -7n Solving 3n2 = -12 + -7n Solving for variable 'n'. Reorder the terms: 12 + 7n + 3n2 = -12 + -7n + 12 + 7n Reorder the terms: 12 + 7n + 3n2 = -12 + 12 + -7n + 7n Combine like terms: -12 + 12 = 0 12 + 7n + 3n2 = 0 + -7n + 7n 12 + 7n + 3n2 = -7n + 7n Combine like terms: -7n + 7n = 0 12 + 7n + 3n2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 4 + 2.333333333n + n2 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + 2.333333333n + -4 + n2 = 0 + -4 Reorder the terms: 4 + -4 + 2.333333333n + n2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 2.333333333n + n2 = 0 + -4 2.333333333n + n2 = 0 + -4 Combine like terms: 0 + -4 = -4 2.333333333n + n2 = -4 The n term is 2.333333333n. Take half its coefficient (1.166666667). Square it (1.361111112) and add it to both sides. Add '1.361111112' to each side of the equation. 2.333333333n + 1.361111112 + n2 = -4 + 1.361111112 Reorder the terms: 1.361111112 + 2.333333333n + n2 = -4 + 1.361111112 Combine like terms: -4 + 1.361111112 = -2.638888888 1.361111112 + 2.333333333n + n2 = -2.638888888 Factor a perfect square on the left side: (n + 1.166666667)(n + 1.166666667) = -2.638888888 Can't calculate square root of the right side. The solution to this equation could not be determined.
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