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Simplifying 4n2 + -8n + 30 = -6 Reorder the terms: 30 + -8n + 4n2 = -6 Solving 30 + -8n + 4n2 = -6 Solving for variable 'n'. Reorder the terms: 30 + 6 + -8n + 4n2 = -6 + 6 Combine like terms: 30 + 6 = 36 36 + -8n + 4n2 = -6 + 6 Combine like terms: -6 + 6 = 0 36 + -8n + 4n2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(9 + -2n + n2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(9 + -2n + n2)' equal to zero and attempt to solve: Simplifying 9 + -2n + n2 = 0 Solving 9 + -2n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '-9' to each side of the equation. 9 + -2n + -9 + n2 = 0 + -9 Reorder the terms: 9 + -9 + -2n + n2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -2n + n2 = 0 + -9 -2n + n2 = 0 + -9 Combine like terms: 0 + -9 = -9 -2n + n2 = -9 The n term is -2n. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2n + 1 + n2 = -9 + 1 Reorder the terms: 1 + -2n + n2 = -9 + 1 Combine like terms: -9 + 1 = -8 1 + -2n + n2 = -8 Factor a perfect square on the left side: (n + -1)(n + -1) = -8 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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