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Simplifying 90 = -6n(2n + -7) Reorder the terms: 90 = -6n(-7 + 2n) 90 = (-7 * -6n + 2n * -6n) 90 = (42n + -12n2) Solving 90 = 42n + -12n2 Solving for variable 'n'. Reorder the terms: 90 + -42n + 12n2 = 42n + -42n + -12n2 + 12n2 Combine like terms: 42n + -42n = 0 90 + -42n + 12n2 = 0 + -12n2 + 12n2 90 + -42n + 12n2 = -12n2 + 12n2 Combine like terms: -12n2 + 12n2 = 0 90 + -42n + 12n2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(15 + -7n + 2n2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(15 + -7n + 2n2)' equal to zero and attempt to solve: Simplifying 15 + -7n + 2n2 = 0 Solving 15 + -7n + 2n2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 7.5 + -3.5n + n2 = 0 Move the constant term to the right: Add '-7.5' to each side of the equation. 7.5 + -3.5n + -7.5 + n2 = 0 + -7.5 Reorder the terms: 7.5 + -7.5 + -3.5n + n2 = 0 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + -3.5n + n2 = 0 + -7.5 -3.5n + n2 = 0 + -7.5 Combine like terms: 0 + -7.5 = -7.5 -3.5n + n2 = -7.5 The n term is -3.5n. Take half its coefficient (-1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. -3.5n + 3.0625 + n2 = -7.5 + 3.0625 Reorder the terms: 3.0625 + -3.5n + n2 = -7.5 + 3.0625 Combine like terms: -7.5 + 3.0625 = -4.4375 3.0625 + -3.5n + n2 = -4.4375 Factor a perfect square on the left side: (n + -1.75)(n + -1.75) = -4.4375 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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