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Simplifying 8 + -1n * n = 20 + n Multiply n * n 8 + -1n2 = 20 + n Solving 8 + -1n2 = 20 + n Solving for variable 'n'. Reorder the terms: 8 + -20 + -1n + -1n2 = 20 + n + -20 + -1n Combine like terms: 8 + -20 = -12 -12 + -1n + -1n2 = 20 + n + -20 + -1n Reorder the terms: -12 + -1n + -1n2 = 20 + -20 + n + -1n Combine like terms: 20 + -20 = 0 -12 + -1n + -1n2 = 0 + n + -1n -12 + -1n + -1n2 = n + -1n Combine like terms: n + -1n = 0 -12 + -1n + -1n2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(12 + n + n2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(12 + n + n2)' equal to zero and attempt to solve: Simplifying 12 + n + n2 = 0 Solving 12 + n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '-12' to each side of the equation. 12 + n + -12 + n2 = 0 + -12 Reorder the terms: 12 + -12 + n + n2 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + n + n2 = 0 + -12 n + n2 = 0 + -12 Combine like terms: 0 + -12 = -12 n + n2 = -12 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 = -12 + 0.25 Reorder the terms: 0.25 + n + n2 = -12 + 0.25 Combine like terms: -12 + 0.25 = -11.75 0.25 + n + n2 = -11.75 Factor a perfect square on the left side: (n + 0.5)(n + 0.5) = -11.75 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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