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Simplifying 30n2 + -21n + 30 = 0 Reorder the terms: 30 + -21n + 30n2 = 0 Solving 30 + -21n + 30n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '3'. 3(10 + -7n + 10n2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(10 + -7n + 10n2)' equal to zero and attempt to solve: Simplifying 10 + -7n + 10n2 = 0 Solving 10 + -7n + 10n2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. 1 + -0.7n + n2 = 0.0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + -0.7n + -1 + n2 = 0.0 + -1 Reorder the terms: 1 + -1 + -0.7n + n2 = 0.0 + -1 Combine like terms: 1 + -1 = 0 0 + -0.7n + n2 = 0.0 + -1 -0.7n + n2 = 0.0 + -1 Combine like terms: 0.0 + -1 = -1 -0.7n + n2 = -1 The n term is -0.7n. Take half its coefficient (-0.35). Square it (0.1225) and add it to both sides. Add '0.1225' to each side of the equation. -0.7n + 0.1225 + n2 = -1 + 0.1225 Reorder the terms: 0.1225 + -0.7n + n2 = -1 + 0.1225 Combine like terms: -1 + 0.1225 = -0.8775 0.1225 + -0.7n + n2 = -0.8775 Factor a perfect square on the left side: (n + -0.35)(n + -0.35) = -0.8775 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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