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Simplifying -1n2 + -10n + -26 = 0 Reorder the terms: -26 + -10n + -1n2 = 0 Solving -26 + -10n + -1n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '-1'. -1(26 + 10n + n2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(26 + 10n + n2)' equal to zero and attempt to solve: Simplifying 26 + 10n + n2 = 0 Solving 26 + 10n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '-26' to each side of the equation. 26 + 10n + -26 + n2 = 0 + -26 Reorder the terms: 26 + -26 + 10n + n2 = 0 + -26 Combine like terms: 26 + -26 = 0 0 + 10n + n2 = 0 + -26 10n + n2 = 0 + -26 Combine like terms: 0 + -26 = -26 10n + n2 = -26 The n term is 10n. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10n + 25 + n2 = -26 + 25 Reorder the terms: 25 + 10n + n2 = -26 + 25 Combine like terms: -26 + 25 = -1 25 + 10n + n2 = -1 Factor a perfect square on the left side: (n + 5)(n + 5) = -1 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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