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Simplifying -1n(4n + 4) = 12 Reorder the terms: -1n(4 + 4n) = 12 (4 * -1n + 4n * -1n) = 12 (-4n + -4n2) = 12 Solving -4n + -4n2 = 12 Solving for variable 'n'. Reorder the terms: -12 + -4n + -4n2 = 12 + -12 Combine like terms: 12 + -12 = 0 -12 + -4n + -4n2 = 0 Factor out the Greatest Common Factor (GCF), '-4'. -4(3 + n + n2) = 0 Ignore the factor -4.Subproblem 1
Set the factor '(3 + n + n2)' equal to zero and attempt to solve: Simplifying 3 + n + n2 = 0 Solving 3 + n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '-3' to each side of the equation. 3 + n + -3 + n2 = 0 + -3 Reorder the terms: 3 + -3 + n + n2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + n + n2 = 0 + -3 n + n2 = 0 + -3 Combine like terms: 0 + -3 = -3 n + n2 = -3 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. n + 0.25 + n2 = -3 + 0.25 Reorder the terms: 0.25 + n + n2 = -3 + 0.25 Combine like terms: -3 + 0.25 = -2.75 0.25 + n + n2 = -2.75 Factor a perfect square on the left side: (n + 0.5)(n + 0.5) = -2.75 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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