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Simplifying 5 + -4n(n + 2) = 18 Reorder the terms: 5 + -4n(2 + n) = 18 5 + (2 * -4n + n * -4n) = 18 5 + (-8n + -4n2) = 18 Solving 5 + -8n + -4n2 = 18 Solving for variable 'n'. Reorder the terms: 5 + -18 + -8n + -4n2 = 18 + -18 Combine like terms: 5 + -18 = -13 -13 + -8n + -4n2 = 18 + -18 Combine like terms: 18 + -18 = 0 -13 + -8n + -4n2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(13 + 8n + 4n2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(13 + 8n + 4n2)' equal to zero and attempt to solve: Simplifying 13 + 8n + 4n2 = 0 Solving 13 + 8n + 4n2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 3.25 + 2n + n2 = 0 Move the constant term to the right: Add '-3.25' to each side of the equation. 3.25 + 2n + -3.25 + n2 = 0 + -3.25 Reorder the terms: 3.25 + -3.25 + 2n + n2 = 0 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + 2n + n2 = 0 + -3.25 2n + n2 = 0 + -3.25 Combine like terms: 0 + -3.25 = -3.25 2n + n2 = -3.25 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 = -3.25 + 1 Reorder the terms: 1 + 2n + n2 = -3.25 + 1 Combine like terms: -3.25 + 1 = -2.25 1 + 2n + n2 = -2.25 Factor a perfect square on the left side: (n + 1)(n + 1) = -2.25 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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