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Simplifying 18n2 + -33n + 1218n2 + -33n + 12 = 0 Reorder the terms: 12 + -33n + -33n + 18n2 + 1218n2 = 0 Combine like terms: -33n + -33n = -66n 12 + -66n + 18n2 + 1218n2 = 0 Combine like terms: 18n2 + 1218n2 = 1236n2 12 + -66n + 1236n2 = 0 Solving 12 + -66n + 1236n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '6'. 6(2 + -11n + 206n2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(2 + -11n + 206n2)' equal to zero and attempt to solve: Simplifying 2 + -11n + 206n2 = 0 Solving 2 + -11n + 206n2 = 0 Begin completing the square. Divide all terms by 206 the coefficient of the squared term: Divide each side by '206'. 0.009708737864 + -0.05339805825n + n2 = 0 Move the constant term to the right: Add '-0.009708737864' to each side of the equation. 0.009708737864 + -0.05339805825n + -0.009708737864 + n2 = 0 + -0.009708737864 Reorder the terms: 0.009708737864 + -0.009708737864 + -0.05339805825n + n2 = 0 + -0.009708737864 Combine like terms: 0.009708737864 + -0.009708737864 = 0.000000000000 0.000000000000 + -0.05339805825n + n2 = 0 + -0.009708737864 -0.05339805825n + n2 = 0 + -0.009708737864 Combine like terms: 0 + -0.009708737864 = -0.009708737864 -0.05339805825n + n2 = -0.009708737864 The n term is -0.05339805825n. Take half its coefficient (-0.02669902913). Square it (0.0007128381565) and add it to both sides. Add '0.0007128381565' to each side of the equation. -0.05339805825n + 0.0007128381565 + n2 = -0.009708737864 + 0.0007128381565 Reorder the terms: 0.0007128381565 + -0.05339805825n + n2 = -0.009708737864 + 0.0007128381565 Combine like terms: -0.009708737864 + 0.0007128381565 = -0.0089958997075 0.0007128381565 + -0.05339805825n + n2 = -0.0089958997075 Factor a perfect square on the left side: (n + -0.02669902913)(n + -0.02669902913) = -0.0089958997075 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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