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Simplifying 2n2 + 12n + 82 = 0 Reorder the terms: 82 + 12n + 2n2 = 0 Solving 82 + 12n + 2n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '2'. 2(41 + 6n + n2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(41 + 6n + n2)' equal to zero and attempt to solve: Simplifying 41 + 6n + n2 = 0 Solving 41 + 6n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '-41' to each side of the equation. 41 + 6n + -41 + n2 = 0 + -41 Reorder the terms: 41 + -41 + 6n + n2 = 0 + -41 Combine like terms: 41 + -41 = 0 0 + 6n + n2 = 0 + -41 6n + n2 = 0 + -41 Combine like terms: 0 + -41 = -41 6n + n2 = -41 The n term is 6n. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6n + 9 + n2 = -41 + 9 Reorder the terms: 9 + 6n + n2 = -41 + 9 Combine like terms: -41 + 9 = -32 9 + 6n + n2 = -32 Factor a perfect square on the left side: (n + 3)(n + 3) = -32 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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