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Simplifying 6n2 + -30n + 42 = 0 Reorder the terms: 42 + -30n + 6n2 = 0 Solving 42 + -30n + 6n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '6'. 6(7 + -5n + n2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(7 + -5n + n2)' equal to zero and attempt to solve: Simplifying 7 + -5n + n2 = 0 Solving 7 + -5n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '-7' to each side of the equation. 7 + -5n + -7 + n2 = 0 + -7 Reorder the terms: 7 + -7 + -5n + n2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -5n + n2 = 0 + -7 -5n + n2 = 0 + -7 Combine like terms: 0 + -7 = -7 -5n + n2 = -7 The n term is -5n. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5n + 6.25 + n2 = -7 + 6.25 Reorder the terms: 6.25 + -5n + n2 = -7 + 6.25 Combine like terms: -7 + 6.25 = -0.75 6.25 + -5n + n2 = -0.75 Factor a perfect square on the left side: (n + -2.5)(n + -2.5) = -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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