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Simplifying 2n2 = 10n + -48 Reorder the terms: 2n2 = -48 + 10n Solving 2n2 = -48 + 10n Solving for variable 'n'. Reorder the terms: 48 + -10n + 2n2 = -48 + 10n + 48 + -10n Reorder the terms: 48 + -10n + 2n2 = -48 + 48 + 10n + -10n Combine like terms: -48 + 48 = 0 48 + -10n + 2n2 = 0 + 10n + -10n 48 + -10n + 2n2 = 10n + -10n Combine like terms: 10n + -10n = 0 48 + -10n + 2n2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(24 + -5n + n2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(24 + -5n + n2)' equal to zero and attempt to solve: Simplifying 24 + -5n + n2 = 0 Solving 24 + -5n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '-24' to each side of the equation. 24 + -5n + -24 + n2 = 0 + -24 Reorder the terms: 24 + -24 + -5n + n2 = 0 + -24 Combine like terms: 24 + -24 = 0 0 + -5n + n2 = 0 + -24 -5n + n2 = 0 + -24 Combine like terms: 0 + -24 = -24 -5n + n2 = -24 The n term is -5n. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5n + 6.25 + n2 = -24 + 6.25 Reorder the terms: 6.25 + -5n + n2 = -24 + 6.25 Combine like terms: -24 + 6.25 = -17.75 6.25 + -5n + n2 = -17.75 Factor a perfect square on the left side: (n + -2.5)(n + -2.5) = -17.75 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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