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Simplifying -1(n + 5) + -11n(1 + n) = 0 Reorder the terms: -1(5 + n) + -11n(1 + n) = 0 (5 * -1 + n * -1) + -11n(1 + n) = 0 (-5 + -1n) + -11n(1 + n) = 0 -5 + -1n + (1 * -11n + n * -11n) = 0 -5 + -1n + (-11n + -11n2) = 0 Combine like terms: -1n + -11n = -12n -5 + -12n + -11n2 = 0 Solving -5 + -12n + -11n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '-1'. -1(5 + 12n + 11n2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(5 + 12n + 11n2)' equal to zero and attempt to solve: Simplifying 5 + 12n + 11n2 = 0 Solving 5 + 12n + 11n2 = 0 Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. 0.4545454545 + 1.090909091n + n2 = 0 Move the constant term to the right: Add '-0.4545454545' to each side of the equation. 0.4545454545 + 1.090909091n + -0.4545454545 + n2 = 0 + -0.4545454545 Reorder the terms: 0.4545454545 + -0.4545454545 + 1.090909091n + n2 = 0 + -0.4545454545 Combine like terms: 0.4545454545 + -0.4545454545 = 0.0000000000 0.0000000000 + 1.090909091n + n2 = 0 + -0.4545454545 1.090909091n + n2 = 0 + -0.4545454545 Combine like terms: 0 + -0.4545454545 = -0.4545454545 1.090909091n + n2 = -0.4545454545 The n term is 1.090909091n. Take half its coefficient (0.5454545455). Square it (0.2975206612) and add it to both sides. Add '0.2975206612' to each side of the equation. 1.090909091n + 0.2975206612 + n2 = -0.4545454545 + 0.2975206612 Reorder the terms: 0.2975206612 + 1.090909091n + n2 = -0.4545454545 + 0.2975206612 Combine like terms: -0.4545454545 + 0.2975206612 = -0.1570247933 0.2975206612 + 1.090909091n + n2 = -0.1570247933 Factor a perfect square on the left side: (n + 0.5454545455)(n + 0.5454545455) = -0.1570247933 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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