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Simplifying 8n + -2n(5n + -8) = 23 + 4n + -3 Reorder the terms: 8n + -2n(-8 + 5n) = 23 + 4n + -3 8n + (-8 * -2n + 5n * -2n) = 23 + 4n + -3 8n + (16n + -10n2) = 23 + 4n + -3 Combine like terms: 8n + 16n = 24n 24n + -10n2 = 23 + 4n + -3 Reorder the terms: 24n + -10n2 = 23 + -3 + 4n Combine like terms: 23 + -3 = 20 24n + -10n2 = 20 + 4n Solving 24n + -10n2 = 20 + 4n Solving for variable 'n'. Reorder the terms: -20 + 24n + -4n + -10n2 = 20 + 4n + -20 + -4n Combine like terms: 24n + -4n = 20n -20 + 20n + -10n2 = 20 + 4n + -20 + -4n Reorder the terms: -20 + 20n + -10n2 = 20 + -20 + 4n + -4n Combine like terms: 20 + -20 = 0 -20 + 20n + -10n2 = 0 + 4n + -4n -20 + 20n + -10n2 = 4n + -4n Combine like terms: 4n + -4n = 0 -20 + 20n + -10n2 = 0 Factor out the Greatest Common Factor (GCF), '10'. 10(-2 + 2n + -1n2) = 0 Ignore the factor 10.Subproblem 1
Set the factor '(-2 + 2n + -1n2)' equal to zero and attempt to solve: Simplifying -2 + 2n + -1n2 = 0 Solving -2 + 2n + -1n2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 2 + -2n + n2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + -2n + -2 + n2 = 0 + -2 Reorder the terms: 2 + -2 + -2n + n2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -2n + n2 = 0 + -2 -2n + n2 = 0 + -2 Combine like terms: 0 + -2 = -2 -2n + n2 = -2 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 = -2 + 1 Reorder the terms: 1 + -2n + n2 = -2 + 1 Combine like terms: -2 + 1 = -1 1 + -2n + n2 = -1 Factor a perfect square on the left side: (n + -1)(n + -1) = -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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