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Simplifying 8k2 + 8 = 2k Reorder the terms: 8 + 8k2 = 2k Solving 8 + 8k2 = 2k Solving for variable 'k'. Reorder the terms: 8 + -2k + 8k2 = 2k + -2k Combine like terms: 2k + -2k = 0 8 + -2k + 8k2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(4 + -1k + 4k2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(4 + -1k + 4k2)' equal to zero and attempt to solve: Simplifying 4 + -1k + 4k2 = 0 Solving 4 + -1k + 4k2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 1 + -0.25k + k2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + -0.25k + -1 + k2 = 0 + -1 Reorder the terms: 1 + -1 + -0.25k + k2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -0.25k + k2 = 0 + -1 -0.25k + k2 = 0 + -1 Combine like terms: 0 + -1 = -1 -0.25k + k2 = -1 The k term is -0.25k. Take half its coefficient (-0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. -0.25k + 0.015625 + k2 = -1 + 0.015625 Reorder the terms: 0.015625 + -0.25k + k2 = -1 + 0.015625 Combine like terms: -1 + 0.015625 = -0.984375 0.015625 + -0.25k + k2 = -0.984375 Factor a perfect square on the left side: (k + -0.125)(k + -0.125) = -0.984375 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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