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Simplifying 4n + -1(n + 4) = 2n(n + 2) + 6 Reorder the terms: 4n + -1(4 + n) = 2n(n + 2) + 6 4n + (4 * -1 + n * -1) = 2n(n + 2) + 6 4n + (-4 + -1n) = 2n(n + 2) + 6 Reorder the terms: -4 + 4n + -1n = 2n(n + 2) + 6 Combine like terms: 4n + -1n = 3n -4 + 3n = 2n(n + 2) + 6 Reorder the terms: -4 + 3n = 2n(2 + n) + 6 -4 + 3n = (2 * 2n + n * 2n) + 6 -4 + 3n = (4n + 2n2) + 6 Reorder the terms: -4 + 3n = 6 + 4n + 2n2 Solving -4 + 3n = 6 + 4n + 2n2 Solving for variable 'n'. Reorder the terms: -4 + -6 + 3n + -4n + -2n2 = 6 + 4n + 2n2 + -6 + -4n + -2n2 Combine like terms: -4 + -6 = -10 -10 + 3n + -4n + -2n2 = 6 + 4n + 2n2 + -6 + -4n + -2n2 Combine like terms: 3n + -4n = -1n -10 + -1n + -2n2 = 6 + 4n + 2n2 + -6 + -4n + -2n2 Reorder the terms: -10 + -1n + -2n2 = 6 + -6 + 4n + -4n + 2n2 + -2n2 Combine like terms: 6 + -6 = 0 -10 + -1n + -2n2 = 0 + 4n + -4n + 2n2 + -2n2 -10 + -1n + -2n2 = 4n + -4n + 2n2 + -2n2 Combine like terms: 4n + -4n = 0 -10 + -1n + -2n2 = 0 + 2n2 + -2n2 -10 + -1n + -2n2 = 2n2 + -2n2 Combine like terms: 2n2 + -2n2 = 0 -10 + -1n + -2n2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(10 + n + 2n2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(10 + n + 2n2)' equal to zero and attempt to solve: Simplifying 10 + n + 2n2 = 0 Solving 10 + n + 2n2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 5 + 0.5n + n2 = 0 Move the constant term to the right: Add '-5' to each side of the equation. 5 + 0.5n + -5 + n2 = 0 + -5 Reorder the terms: 5 + -5 + 0.5n + n2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 0.5n + n2 = 0 + -5 0.5n + n2 = 0 + -5 Combine like terms: 0 + -5 = -5 0.5n + n2 = -5 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. 0.5n + 0.25 + n2 = -5 + 0.25 Reorder the terms: 0.25 + 0.5n + n2 = -5 + 0.25 Combine like terms: -5 + 0.25 = -4.75 0.25 + 0.5n + n2 = -4.75 Factor a perfect square on the left side: (n + 0.5)(n + 0.5) = -4.75 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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