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Simplifying -6n(8 + 4n) = 168 (8 * -6n + 4n * -6n) = 168 (-48n + -24n2) = 168 Solving -48n + -24n2 = 168 Solving for variable 'n'. Reorder the terms: -168 + -48n + -24n2 = 168 + -168 Combine like terms: 168 + -168 = 0 -168 + -48n + -24n2 = 0 Factor out the Greatest Common Factor (GCF), '-24'. -24(7 + 2n + n2) = 0 Ignore the factor -24.Subproblem 1
Set the factor '(7 + 2n + n2)' equal to zero and attempt to solve: Simplifying 7 + 2n + n2 = 0 Solving 7 + 2n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '-7' to each side of the equation. 7 + 2n + -7 + n2 = 0 + -7 Reorder the terms: 7 + -7 + 2n + n2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 2n + n2 = 0 + -7 2n + n2 = 0 + -7 Combine like terms: 0 + -7 = -7 2n + n2 = -7 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 = -7 + 1 Reorder the terms: 1 + 2n + n2 = -7 + 1 Combine like terms: -7 + 1 = -6 1 + 2n + n2 = -6 Factor a perfect square on the left side: (n + 1)(n + 1) = -6 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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