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Simplifying 2k2 + -6k + 18 = 0 Reorder the terms: 18 + -6k + 2k2 = 0 Solving 18 + -6k + 2k2 = 0 Solving for variable 'k'. Factor out the Greatest Common Factor (GCF), '2'. 2(9 + -3k + k2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(9 + -3k + k2)' equal to zero and attempt to solve: Simplifying 9 + -3k + k2 = 0 Solving 9 + -3k + k2 = 0 Begin completing the square. Move the constant term to the right: Add '-9' to each side of the equation. 9 + -3k + -9 + k2 = 0 + -9 Reorder the terms: 9 + -9 + -3k + k2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -3k + k2 = 0 + -9 -3k + k2 = 0 + -9 Combine like terms: 0 + -9 = -9 -3k + k2 = -9 The k term is -3k. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3k + 2.25 + k2 = -9 + 2.25 Reorder the terms: 2.25 + -3k + k2 = -9 + 2.25 Combine like terms: -9 + 2.25 = -6.75 2.25 + -3k + k2 = -6.75 Factor a perfect square on the left side: (k + -1.5)(k + -1.5) = -6.75 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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