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Simplifying 36n2 + -16n + 28 = 0 Reorder the terms: 28 + -16n + 36n2 = 0 Solving 28 + -16n + 36n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '4'. 4(7 + -4n + 9n2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(7 + -4n + 9n2)' equal to zero and attempt to solve: Simplifying 7 + -4n + 9n2 = 0 Solving 7 + -4n + 9n2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 0.7777777778 + -0.4444444444n + n2 = 0 Move the constant term to the right: Add '-0.7777777778' to each side of the equation. 0.7777777778 + -0.4444444444n + -0.7777777778 + n2 = 0 + -0.7777777778 Reorder the terms: 0.7777777778 + -0.7777777778 + -0.4444444444n + n2 = 0 + -0.7777777778 Combine like terms: 0.7777777778 + -0.7777777778 = 0.0000000000 0.0000000000 + -0.4444444444n + n2 = 0 + -0.7777777778 -0.4444444444n + n2 = 0 + -0.7777777778 Combine like terms: 0 + -0.7777777778 = -0.7777777778 -0.4444444444n + n2 = -0.7777777778 The n term is -0.4444444444n. Take half its coefficient (-0.2222222222). Square it (0.04938271604) and add it to both sides. Add '0.04938271604' to each side of the equation. -0.4444444444n + 0.04938271604 + n2 = -0.7777777778 + 0.04938271604 Reorder the terms: 0.04938271604 + -0.4444444444n + n2 = -0.7777777778 + 0.04938271604 Combine like terms: -0.7777777778 + 0.04938271604 = -0.72839506176 0.04938271604 + -0.4444444444n + n2 = -0.72839506176 Factor a perfect square on the left side: (n + -0.2222222222)(n + -0.2222222222) = -0.72839506176 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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