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Simplifying -12n2 + -11n + -15 = 0 Reorder the terms: -15 + -11n + -12n2 = 0 Solving -15 + -11n + -12n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '-1'. -1(15 + 11n + 12n2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(15 + 11n + 12n2)' equal to zero and attempt to solve: Simplifying 15 + 11n + 12n2 = 0 Solving 15 + 11n + 12n2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. 1.25 + 0.9166666667n + n2 = 0 Move the constant term to the right: Add '-1.25' to each side of the equation. 1.25 + 0.9166666667n + -1.25 + n2 = 0 + -1.25 Reorder the terms: 1.25 + -1.25 + 0.9166666667n + n2 = 0 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + 0.9166666667n + n2 = 0 + -1.25 0.9166666667n + n2 = 0 + -1.25 Combine like terms: 0 + -1.25 = -1.25 0.9166666667n + n2 = -1.25 The n term is 0.9166666667n. Take half its coefficient (0.4583333334). Square it (0.2100694445) and add it to both sides. Add '0.2100694445' to each side of the equation. 0.9166666667n + 0.2100694445 + n2 = -1.25 + 0.2100694445 Reorder the terms: 0.2100694445 + 0.9166666667n + n2 = -1.25 + 0.2100694445 Combine like terms: -1.25 + 0.2100694445 = -1.0399305555 0.2100694445 + 0.9166666667n + n2 = -1.0399305555 Factor a perfect square on the left side: (n + 0.4583333334)(n + 0.4583333334) = -1.0399305555 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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