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Simplifying 30 = -5n(6n + 6) Reorder the terms: 30 = -5n(6 + 6n) 30 = (6 * -5n + 6n * -5n) 30 = (-30n + -30n2) Solving 30 = -30n + -30n2 Solving for variable 'n'. Reorder the terms: 30 + 30n + 30n2 = -30n + 30n + -30n2 + 30n2 Combine like terms: -30n + 30n = 0 30 + 30n + 30n2 = 0 + -30n2 + 30n2 30 + 30n + 30n2 = -30n2 + 30n2 Combine like terms: -30n2 + 30n2 = 0 30 + 30n + 30n2 = 0 Factor out the Greatest Common Factor (GCF), '30'. 30(1 + n + n2) = 0 Ignore the factor 30.Subproblem 1
Set the factor '(1 + n + n2)' equal to zero and attempt to solve: Simplifying 1 + n + n2 = 0 Solving 1 + n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + n + -1 + n2 = 0 + -1 Reorder the terms: 1 + -1 + n + n2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + n + n2 = 0 + -1 n + n2 = 0 + -1 Combine like terms: 0 + -1 = -1 n + n2 = -1 The n term is n. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. n + 0.25 + n2 = -1 + 0.25 Reorder the terms: 0.25 + n + n2 = -1 + 0.25 Combine like terms: -1 + 0.25 = -0.75 0.25 + n + n2 = -0.75 Factor a perfect square on the left side: (n + 0.5)(n + 0.5) = -0.75 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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