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Simplifying n2 + 12n2 + 48n + 64 = 0 Reorder the terms: 64 + 48n + n2 + 12n2 = 0 Combine like terms: n2 + 12n2 = 13n2 64 + 48n + 13n2 = 0 Solving 64 + 48n + 13n2 = 0 Solving for variable 'n'. Begin completing the square. Divide all terms by 13 the coefficient of the squared term: Divide each side by '13'. 4.923076923 + 3.692307692n + n2 = 0 Move the constant term to the right: Add '-4.923076923' to each side of the equation. 4.923076923 + 3.692307692n + -4.923076923 + n2 = 0 + -4.923076923 Reorder the terms: 4.923076923 + -4.923076923 + 3.692307692n + n2 = 0 + -4.923076923 Combine like terms: 4.923076923 + -4.923076923 = 0.000000000 0.000000000 + 3.692307692n + n2 = 0 + -4.923076923 3.692307692n + n2 = 0 + -4.923076923 Combine like terms: 0 + -4.923076923 = -4.923076923 3.692307692n + n2 = -4.923076923 The n term is 3.692307692n. Take half its coefficient (1.846153846). Square it (3.408284023) and add it to both sides. Add '3.408284023' to each side of the equation. 3.692307692n + 3.408284023 + n2 = -4.923076923 + 3.408284023 Reorder the terms: 3.408284023 + 3.692307692n + n2 = -4.923076923 + 3.408284023 Combine like terms: -4.923076923 + 3.408284023 = -1.5147929 3.408284023 + 3.692307692n + n2 = -1.5147929 Factor a perfect square on the left side: (n + 1.846153846)(n + 1.846153846) = -1.5147929 Can't calculate square root of the right side. The solution to this equation could not be determined.
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