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Simplifying 4k2 + 4k + 8 = 0 Reorder the terms: 8 + 4k + 4k2 = 0 Solving 8 + 4k + 4k2 = 0 Solving for variable 'k'. Factor out the Greatest Common Factor (GCF), '4'. 4(2 + k + k2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(2 + k + k2)' equal to zero and attempt to solve: Simplifying 2 + k + k2 = 0 Solving 2 + k + k2 = 0 Begin completing the square. Move the constant term to the right: Add '-2' to each side of the equation. 2 + k + -2 + k2 = 0 + -2 Reorder the terms: 2 + -2 + k + k2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + k + k2 = 0 + -2 k + k2 = 0 + -2 Combine like terms: 0 + -2 = -2 k + k2 = -2 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 = -2 + 0.25 Reorder the terms: 0.25 + k + k2 = -2 + 0.25 Combine like terms: -2 + 0.25 = -1.75 0.25 + k + k2 = -1.75 Factor a perfect square on the left side: (k + 0.5)(k + 0.5) = -1.75 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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