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Simplifying (n) = n2 + 4 + 2n n = n2 + 4 + 2n Reorder the terms: n = 4 + 2n + n2 Solving n = 4 + 2n + n2 Solving for variable 'n'. Reorder the terms: -4 + n + -2n + -1n2 = 4 + 2n + n2 + -4 + -2n + -1n2 Combine like terms: n + -2n = -1n -4 + -1n + -1n2 = 4 + 2n + n2 + -4 + -2n + -1n2 Reorder the terms: -4 + -1n + -1n2 = 4 + -4 + 2n + -2n + n2 + -1n2 Combine like terms: 4 + -4 = 0 -4 + -1n + -1n2 = 0 + 2n + -2n + n2 + -1n2 -4 + -1n + -1n2 = 2n + -2n + n2 + -1n2 Combine like terms: 2n + -2n = 0 -4 + -1n + -1n2 = 0 + n2 + -1n2 -4 + -1n + -1n2 = n2 + -1n2 Combine like terms: n2 + -1n2 = 0 -4 + -1n + -1n2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(4 + n + n2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(4 + n + n2)' equal to zero and attempt to solve: Simplifying 4 + n + n2 = 0 Solving 4 + n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '-4' to each side of the equation. 4 + n + -4 + n2 = 0 + -4 Reorder the terms: 4 + -4 + n + n2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + n + n2 = 0 + -4 n + n2 = 0 + -4 Combine like terms: 0 + -4 = -4 n + n2 = -4 The n term is n. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. n + 0.25 + n2 = -4 + 0.25 Reorder the terms: 0.25 + n + n2 = -4 + 0.25 Combine like terms: -4 + 0.25 = -3.75 0.25 + n + n2 = -3.75 Factor a perfect square on the left side: (n + 0.5)(n + 0.5) = -3.75 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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