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Simplifying -24 + -2n + -1n2 = 0 Solving -24 + -2n + -1n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '-1'. -1(24 + 2n + n2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(24 + 2n + n2)' equal to zero and attempt to solve: Simplifying 24 + 2n + n2 = 0 Solving 24 + 2n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '-24' to each side of the equation. 24 + 2n + -24 + n2 = 0 + -24 Reorder the terms: 24 + -24 + 2n + n2 = 0 + -24 Combine like terms: 24 + -24 = 0 0 + 2n + n2 = 0 + -24 2n + n2 = 0 + -24 Combine like terms: 0 + -24 = -24 2n + n2 = -24 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 = -24 + 1 Reorder the terms: 1 + 2n + n2 = -24 + 1 Combine like terms: -24 + 1 = -23 1 + 2n + n2 = -23 Factor a perfect square on the left side: (n + 1)(n + 1) = -23 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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