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Simplifying 0 = 10(n2 + n) + -6(n2 + -2) Reorder the terms: 0 = 10(n + n2) + -6(n2 + -2) 0 = (n * 10 + n2 * 10) + -6(n2 + -2) 0 = (10n + 10n2) + -6(n2 + -2) Reorder the terms: 0 = 10n + 10n2 + -6(-2 + n2) 0 = 10n + 10n2 + (-2 * -6 + n2 * -6) 0 = 10n + 10n2 + (12 + -6n2) Reorder the terms: 0 = 12 + 10n + 10n2 + -6n2 Combine like terms: 10n2 + -6n2 = 4n2 0 = 12 + 10n + 4n2 Solving 0 = 12 + 10n + 4n2 Solving for variable 'n'. Combine like terms: 0 + -12 = -12 -12 + -10n + -4n2 = 12 + 10n + 4n2 + -12 + -10n + -4n2 Reorder the terms: -12 + -10n + -4n2 = 12 + -12 + 10n + -10n + 4n2 + -4n2 Combine like terms: 12 + -12 = 0 -12 + -10n + -4n2 = 0 + 10n + -10n + 4n2 + -4n2 -12 + -10n + -4n2 = 10n + -10n + 4n2 + -4n2 Combine like terms: 10n + -10n = 0 -12 + -10n + -4n2 = 0 + 4n2 + -4n2 -12 + -10n + -4n2 = 4n2 + -4n2 Combine like terms: 4n2 + -4n2 = 0 -12 + -10n + -4n2 = 0 Factor out the Greatest Common Factor (GCF), '-2'. -2(6 + 5n + 2n2) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(6 + 5n + 2n2)' equal to zero and attempt to solve: Simplifying 6 + 5n + 2n2 = 0 Solving 6 + 5n + 2n2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 3 + 2.5n + n2 = 0 Move the constant term to the right: Add '-3' to each side of the equation. 3 + 2.5n + -3 + n2 = 0 + -3 Reorder the terms: 3 + -3 + 2.5n + n2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2.5n + n2 = 0 + -3 2.5n + n2 = 0 + -3 Combine like terms: 0 + -3 = -3 2.5n + n2 = -3 The n term is 2.5n. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5n + 1.5625 + n2 = -3 + 1.5625 Reorder the terms: 1.5625 + 2.5n + n2 = -3 + 1.5625 Combine like terms: -3 + 1.5625 = -1.4375 1.5625 + 2.5n + n2 = -1.4375 Factor a perfect square on the left side: (n + 1.25)(n + 1.25) = -1.4375 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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