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Simplifying 10n2 + 45 = 5n Reorder the terms: 45 + 10n2 = 5n Solving 45 + 10n2 = 5n Solving for variable 'n'. Reorder the terms: 45 + -5n + 10n2 = 5n + -5n Combine like terms: 5n + -5n = 0 45 + -5n + 10n2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(9 + -1n + 2n2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(9 + -1n + 2n2)' equal to zero and attempt to solve: Simplifying 9 + -1n + 2n2 = 0 Solving 9 + -1n + 2n2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 4.5 + -0.5n + n2 = 0 Move the constant term to the right: Add '-4.5' to each side of the equation. 4.5 + -0.5n + -4.5 + n2 = 0 + -4.5 Reorder the terms: 4.5 + -4.5 + -0.5n + n2 = 0 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + -0.5n + n2 = 0 + -4.5 -0.5n + n2 = 0 + -4.5 Combine like terms: 0 + -4.5 = -4.5 -0.5n + n2 = -4.5 The n term is -0.5n. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5n + 0.0625 + n2 = -4.5 + 0.0625 Reorder the terms: 0.0625 + -0.5n + n2 = -4.5 + 0.0625 Combine like terms: -4.5 + 0.0625 = -4.4375 0.0625 + -0.5n + n2 = -4.4375 Factor a perfect square on the left side: (n + -0.25)(n + -0.25) = -4.4375 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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