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Simplifying 5(4 + 2n + n2) = 0 (4 * 5 + 2n * 5 + n2 * 5) = 0 (20 + 10n + 5n2) = 0 Solving 20 + 10n + 5n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '5'. 5(4 + 2n + n2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(4 + 2n + n2)' equal to zero and attempt to solve: Simplifying 4 + 2n + n2 = 0 Solving 4 + 2n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '-4' to each side of the equation. 4 + 2n + -4 + n2 = 0 + -4 Reorder the terms: 4 + -4 + 2n + n2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 2n + n2 = 0 + -4 2n + n2 = 0 + -4 Combine like terms: 0 + -4 = -4 2n + n2 = -4 The n term is 2n. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2n + 1 + n2 = -4 + 1 Reorder the terms: 1 + 2n + n2 = -4 + 1 Combine like terms: -4 + 1 = -3 1 + 2n + n2 = -3 Factor a perfect square on the left side: (n + 1)(n + 1) = -3 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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