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Simplifying -5n(6n + 6) = 30 Reorder the terms: -5n(6 + 6n) = 30 (6 * -5n + 6n * -5n) = 30 (-30n + -30n2) = 30 Solving -30n + -30n2 = 30 Solving for variable 'n'. Reorder the terms: -30 + -30n + -30n2 = 30 + -30 Combine like terms: 30 + -30 = 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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