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Simplifying 6n2 + -10n + 10 = 0 Reorder the terms: 10 + -10n + 6n2 = 0 Solving 10 + -10n + 6n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '2'. 2(5 + -5n + 3n2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(5 + -5n + 3n2)' equal to zero and attempt to solve: Simplifying 5 + -5n + 3n2 = 0 Solving 5 + -5n + 3n2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 1.666666667 + -1.666666667n + n2 = 0 Move the constant term to the right: Add '-1.666666667' to each side of the equation. 1.666666667 + -1.666666667n + -1.666666667 + n2 = 0 + -1.666666667 Reorder the terms: 1.666666667 + -1.666666667 + -1.666666667n + n2 = 0 + -1.666666667 Combine like terms: 1.666666667 + -1.666666667 = 0.000000000 0.000000000 + -1.666666667n + n2 = 0 + -1.666666667 -1.666666667n + n2 = 0 + -1.666666667 Combine like terms: 0 + -1.666666667 = -1.666666667 -1.666666667n + n2 = -1.666666667 The n term is -1.666666667n. Take half its coefficient (-0.8333333335). Square it (0.6944444447) and add it to both sides. Add '0.6944444447' to each side of the equation. -1.666666667n + 0.6944444447 + n2 = -1.666666667 + 0.6944444447 Reorder the terms: 0.6944444447 + -1.666666667n + n2 = -1.666666667 + 0.6944444447 Combine like terms: -1.666666667 + 0.6944444447 = -0.9722222223 0.6944444447 + -1.666666667n + n2 = -0.9722222223 Factor a perfect square on the left side: (n + -0.8333333335)(n + -0.8333333335) = -0.9722222223 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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