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Simplifying -2n(4n + 4) = 10 Reorder the terms: -2n(4 + 4n) = 10 (4 * -2n + 4n * -2n) = 10 (-8n + -8n2) = 10 Solving -8n + -8n2 = 10 Solving for variable 'n'. Reorder the terms: -10 + -8n + -8n2 = 10 + -10 Combine like terms: 10 + -10 = 0 -10 + -8n + -8n2 = 0 Factor out the Greatest Common Factor (GCF), '-2'. -2(5 + 4n + 4n2) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(5 + 4n + 4n2)' equal to zero and attempt to solve: Simplifying 5 + 4n + 4n2 = 0 Solving 5 + 4n + 4n2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 1.25 + n + n2 = 0 Move the constant term to the right: Add '-1.25' to each side of the equation. 1.25 + n + -1.25 + n2 = 0 + -1.25 Reorder the terms: 1.25 + -1.25 + n + n2 = 0 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + n + n2 = 0 + -1.25 n + n2 = 0 + -1.25 Combine like terms: 0 + -1.25 = -1.25 n + n2 = -1.25 The n term is n. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + n2 = -1.25 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + n2 = -1.25 + 0.25 Combine like terms: -1.25 + 0.25 = -1 1.25 + n2 = -1 Factor a perfect square on the left side: (n + 0.5)(n + 0.5) = -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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