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Simplifying 2k2 + 2k + 8 = 0 Reorder the terms: 8 + 2k + 2k2 = 0 Solving 8 + 2k + 2k2 = 0 Solving for variable 'k'. Factor out the Greatest Common Factor (GCF), '2'. 2(4 + k + k2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(4 + k + k2)' equal to zero and attempt to solve: Simplifying 4 + k + k2 = 0 Solving 4 + k + k2 = 0 Begin completing the square. Move the constant term to the right: Add '-4' to each side of the equation. 4 + k + -4 + k2 = 0 + -4 Reorder the terms: 4 + -4 + k + k2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + k + k2 = 0 + -4 k + k2 = 0 + -4 Combine like terms: 0 + -4 = -4 k + k2 = -4 The k term is k. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. k + 0.25 + k2 = -4 + 0.25 Reorder the terms: 0.25 + k + k2 = -4 + 0.25 Combine like terms: -4 + 0.25 = -3.75 0.25 + k + k2 = -3.75 Factor a perfect square on the left side: (k + 0.5)(k + 0.5) = -3.75 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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