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Simplifying 4k2 + 16k + 77 = -5 Reorder the terms: 77 + 16k + 4k2 = -5 Solving 77 + 16k + 4k2 = -5 Solving for variable 'k'. Reorder the terms: 77 + 5 + 16k + 4k2 = -5 + 5 Combine like terms: 77 + 5 = 82 82 + 16k + 4k2 = -5 + 5 Combine like terms: -5 + 5 = 0 82 + 16k + 4k2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(41 + 8k + 2k2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(41 + 8k + 2k2)' equal to zero and attempt to solve: Simplifying 41 + 8k + 2k2 = 0 Solving 41 + 8k + 2k2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 20.5 + 4k + k2 = 0 Move the constant term to the right: Add '-20.5' to each side of the equation. 20.5 + 4k + -20.5 + k2 = 0 + -20.5 Reorder the terms: 20.5 + -20.5 + 4k + k2 = 0 + -20.5 Combine like terms: 20.5 + -20.5 = 0.0 0.0 + 4k + k2 = 0 + -20.5 4k + k2 = 0 + -20.5 Combine like terms: 0 + -20.5 = -20.5 4k + k2 = -20.5 The k term is 4k. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4k + 4 + k2 = -20.5 + 4 Reorder the terms: 4 + 4k + k2 = -20.5 + 4 Combine like terms: -20.5 + 4 = -16.5 4 + 4k + k2 = -16.5 Factor a perfect square on the left side: (k + 2)(k + 2) = -16.5 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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