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Simplifying 2k2 + 6 = 4k Reorder the terms: 6 + 2k2 = 4k Solving 6 + 2k2 = 4k Solving for variable 'k'. Reorder the terms: 6 + -4k + 2k2 = 4k + -4k Combine like terms: 4k + -4k = 0 6 + -4k + 2k2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(3 + -2k + k2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(3 + -2k + k2)' equal to zero and attempt to solve: Simplifying 3 + -2k + k2 = 0 Solving 3 + -2k + k2 = 0 Begin completing the square. Move the constant term to the right: Add '-3' to each side of the equation. 3 + -2k + -3 + k2 = 0 + -3 Reorder the terms: 3 + -3 + -2k + k2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2k + k2 = 0 + -3 -2k + k2 = 0 + -3 Combine like terms: 0 + -3 = -3 -2k + k2 = -3 The k term is -2k. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2k + 1 + k2 = -3 + 1 Reorder the terms: 1 + -2k + k2 = -3 + 1 Combine like terms: -3 + 1 = -2 1 + -2k + k2 = -2 Factor a perfect square on the left side: (k + -1)(k + -1) = -2 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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