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Simplifying -4n(2n + 3) = 8 Reorder the terms: -4n(3 + 2n) = 8 (3 * -4n + 2n * -4n) = 8 (-12n + -8n2) = 8 Solving -12n + -8n2 = 8 Solving for variable 'n'. Reorder the terms: -8 + -12n + -8n2 = 8 + -8 Combine like terms: 8 + -8 = 0 -8 + -12n + -8n2 = 0 Factor out the Greatest Common Factor (GCF), '-4'. -4(2 + 3n + 2n2) = 0 Ignore the factor -4.Subproblem 1
Set the factor '(2 + 3n + 2n2)' equal to zero and attempt to solve: Simplifying 2 + 3n + 2n2 = 0 Solving 2 + 3n + 2n2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 1 + 1.5n + n2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + 1.5n + -1 + n2 = 0 + -1 Reorder the terms: 1 + -1 + 1.5n + n2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 1.5n + n2 = 0 + -1 1.5n + n2 = 0 + -1 Combine like terms: 0 + -1 = -1 1.5n + n2 = -1 The n term is 1.5n. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5n + 0.5625 + n2 = -1 + 0.5625 Reorder the terms: 0.5625 + 1.5n + n2 = -1 + 0.5625 Combine like terms: -1 + 0.5625 = -0.4375 0.5625 + 1.5n + n2 = -0.4375 Factor a perfect square on the left side: (n + 0.75)(n + 0.75) = -0.4375 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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