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Simplifying (8n2 + -11n + 7) + (7n2 + 2n + -4) = 0 Reorder the terms: (7 + -11n + 8n2) + (7n2 + 2n + -4) = 0 Remove parenthesis around (7 + -11n + 8n2) 7 + -11n + 8n2 + (7n2 + 2n + -4) = 0 Reorder the terms: 7 + -11n + 8n2 + (-4 + 2n + 7n2) = 0 Remove parenthesis around (-4 + 2n + 7n2) 7 + -11n + 8n2 + -4 + 2n + 7n2 = 0 Reorder the terms: 7 + -4 + -11n + 2n + 8n2 + 7n2 = 0 Combine like terms: 7 + -4 = 3 3 + -11n + 2n + 8n2 + 7n2 = 0 Combine like terms: -11n + 2n = -9n 3 + -9n + 8n2 + 7n2 = 0 Combine like terms: 8n2 + 7n2 = 15n2 3 + -9n + 15n2 = 0 Solving 3 + -9n + 15n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '3'. 3(1 + -3n + 5n2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(1 + -3n + 5n2)' equal to zero and attempt to solve: Simplifying 1 + -3n + 5n2 = 0 Solving 1 + -3n + 5n2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.2 + -0.6n + n2 = 0 Move the constant term to the right: Add '-0.2' to each side of the equation. 0.2 + -0.6n + -0.2 + n2 = 0 + -0.2 Reorder the terms: 0.2 + -0.2 + -0.6n + n2 = 0 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + -0.6n + n2 = 0 + -0.2 -0.6n + n2 = 0 + -0.2 Combine like terms: 0 + -0.2 = -0.2 -0.6n + n2 = -0.2 The n term is -0.6n. Take half its coefficient (-0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. -0.6n + 0.09 + n2 = -0.2 + 0.09 Reorder the terms: 0.09 + -0.6n + n2 = -0.2 + 0.09 Combine like terms: -0.2 + 0.09 = -0.11 0.09 + -0.6n + n2 = -0.11 Factor a perfect square on the left side: (n + -0.3)(n + -0.3) = -0.11 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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