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Simplifying 0 = 82n2 + -27n + 162 Reorder the terms: 0 = 162 + -27n + 82n2 Solving 0 = 162 + -27n + 82n2 Solving for variable 'n'. Combine like terms: 0 + -162 = -162 -162 + 27n + -82n2 = 162 + -27n + 82n2 + -162 + 27n + -82n2 Reorder the terms: -162 + 27n + -82n2 = 162 + -162 + -27n + 27n + 82n2 + -82n2 Combine like terms: 162 + -162 = 0 -162 + 27n + -82n2 = 0 + -27n + 27n + 82n2 + -82n2 -162 + 27n + -82n2 = -27n + 27n + 82n2 + -82n2 Combine like terms: -27n + 27n = 0 -162 + 27n + -82n2 = 0 + 82n2 + -82n2 -162 + 27n + -82n2 = 82n2 + -82n2 Combine like terms: 82n2 + -82n2 = 0 -162 + 27n + -82n2 = 0 Begin completing the square. Divide all terms by -82 the coefficient of the squared term: Divide each side by '-82'. 1.975609756 + -0.3292682927n + n2 = 0 Move the constant term to the right: Add '-1.975609756' to each side of the equation. 1.975609756 + -0.3292682927n + -1.975609756 + n2 = 0 + -1.975609756 Reorder the terms: 1.975609756 + -1.975609756 + -0.3292682927n + n2 = 0 + -1.975609756 Combine like terms: 1.975609756 + -1.975609756 = 0.000000000 0.000000000 + -0.3292682927n + n2 = 0 + -1.975609756 -0.3292682927n + n2 = 0 + -1.975609756 Combine like terms: 0 + -1.975609756 = -1.975609756 -0.3292682927n + n2 = -1.975609756 The n term is -0.3292682927n. Take half its coefficient (-0.1646341464). Square it (0.02710440216) and add it to both sides. Add '0.02710440216' to each side of the equation. -0.3292682927n + 0.02710440216 + n2 = -1.975609756 + 0.02710440216 Reorder the terms: 0.02710440216 + -0.3292682927n + n2 = -1.975609756 + 0.02710440216 Combine like terms: -1.975609756 + 0.02710440216 = -1.94850535384 0.02710440216 + -0.3292682927n + n2 = -1.94850535384 Factor a perfect square on the left side: (n + -0.1646341464)(n + -0.1646341464) = -1.94850535384 Can't calculate square root of the right side. The solution to this equation could not be determined.
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