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Simplifying 8k2 + 6k + 10 = 0 Reorder the terms: 10 + 6k + 8k2 = 0 Solving 10 + 6k + 8k2 = 0 Solving for variable 'k'. Factor out the Greatest Common Factor (GCF), '2'. 2(5 + 3k + 4k2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(5 + 3k + 4k2)' equal to zero and attempt to solve: Simplifying 5 + 3k + 4k2 = 0 Solving 5 + 3k + 4k2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 1.25 + 0.75k + k2 = 0 Move the constant term to the right: Add '-1.25' to each side of the equation. 1.25 + 0.75k + -1.25 + k2 = 0 + -1.25 Reorder the terms: 1.25 + -1.25 + 0.75k + k2 = 0 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + 0.75k + k2 = 0 + -1.25 0.75k + k2 = 0 + -1.25 Combine like terms: 0 + -1.25 = -1.25 0.75k + k2 = -1.25 The k term is 0.75k. Take half its coefficient (0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. 0.75k + 0.140625 + k2 = -1.25 + 0.140625 Reorder the terms: 0.140625 + 0.75k + k2 = -1.25 + 0.140625 Combine like terms: -1.25 + 0.140625 = -1.109375 0.140625 + 0.75k + k2 = -1.109375 Factor a perfect square on the left side: (k + 0.375)(k + 0.375) = -1.109375 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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