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Simplifying 0 = 28n2 + -9n + 54 Reorder the terms: 0 = 54 + -9n + 28n2 Solving 0 = 54 + -9n + 28n2 Solving for variable 'n'. Combine like terms: 0 + -54 = -54 -54 + 9n + -28n2 = 54 + -9n + 28n2 + -54 + 9n + -28n2 Reorder the terms: -54 + 9n + -28n2 = 54 + -54 + -9n + 9n + 28n2 + -28n2 Combine like terms: 54 + -54 = 0 -54 + 9n + -28n2 = 0 + -9n + 9n + 28n2 + -28n2 -54 + 9n + -28n2 = -9n + 9n + 28n2 + -28n2 Combine like terms: -9n + 9n = 0 -54 + 9n + -28n2 = 0 + 28n2 + -28n2 -54 + 9n + -28n2 = 28n2 + -28n2 Combine like terms: 28n2 + -28n2 = 0 -54 + 9n + -28n2 = 0 Begin completing the square. Divide all terms by -28 the coefficient of the squared term: Divide each side by '-28'. 1.928571429 + -0.3214285714n + n2 = 0 Move the constant term to the right: Add '-1.928571429' to each side of the equation. 1.928571429 + -0.3214285714n + -1.928571429 + n2 = 0 + -1.928571429 Reorder the terms: 1.928571429 + -1.928571429 + -0.3214285714n + n2 = 0 + -1.928571429 Combine like terms: 1.928571429 + -1.928571429 = 0.000000000 0.000000000 + -0.3214285714n + n2 = 0 + -1.928571429 -0.3214285714n + n2 = 0 + -1.928571429 Combine like terms: 0 + -1.928571429 = -1.928571429 -0.3214285714n + n2 = -1.928571429 The n term is -0.3214285714n. Take half its coefficient (-0.1607142857). Square it (0.02582908163) and add it to both sides. Add '0.02582908163' to each side of the equation. -0.3214285714n + 0.02582908163 + n2 = -1.928571429 + 0.02582908163 Reorder the terms: 0.02582908163 + -0.3214285714n + n2 = -1.928571429 + 0.02582908163 Combine like terms: -1.928571429 + 0.02582908163 = -1.90274234737 0.02582908163 + -0.3214285714n + n2 = -1.90274234737 Factor a perfect square on the left side: (n + -0.1607142857)(n + -0.1607142857) = -1.90274234737 Can't calculate square root of the right side. The solution to this equation could not be determined.
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