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Simplifying 17k2 + -10k + -6 = 7k2 + -11 Reorder the terms: -6 + -10k + 17k2 = 7k2 + -11 Reorder the terms: -6 + -10k + 17k2 = -11 + 7k2 Solving -6 + -10k + 17k2 = -11 + 7k2 Solving for variable 'k'. Reorder the terms: -6 + 11 + -10k + 17k2 + -7k2 = -11 + 7k2 + 11 + -7k2 Combine like terms: -6 + 11 = 5 5 + -10k + 17k2 + -7k2 = -11 + 7k2 + 11 + -7k2 Combine like terms: 17k2 + -7k2 = 10k2 5 + -10k + 10k2 = -11 + 7k2 + 11 + -7k2 Reorder the terms: 5 + -10k + 10k2 = -11 + 11 + 7k2 + -7k2 Combine like terms: -11 + 11 = 0 5 + -10k + 10k2 = 0 + 7k2 + -7k2 5 + -10k + 10k2 = 7k2 + -7k2 Combine like terms: 7k2 + -7k2 = 0 5 + -10k + 10k2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(1 + -2k + 2k2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(1 + -2k + 2k2)' equal to zero and attempt to solve: Simplifying 1 + -2k + 2k2 = 0 Solving 1 + -2k + 2k2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 0.5 + -1k + k2 = 0 Move the constant term to the right: Add '-0.5' to each side of the equation. 0.5 + -1k + -0.5 + k2 = 0 + -0.5 Reorder the terms: 0.5 + -0.5 + -1k + k2 = 0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + -1k + k2 = 0 + -0.5 -1k + k2 = 0 + -0.5 Combine like terms: 0 + -0.5 = -0.5 -1k + k2 = -0.5 The k term is -1k. 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. -1k + 0.25 + k2 = -0.5 + 0.25 Reorder the terms: 0.25 + -1k + k2 = -0.5 + 0.25 Combine like terms: -0.5 + 0.25 = -0.25 0.25 + -1k + k2 = -0.25 Factor a perfect square on the left side: (k + -0.5)(k + -0.5) = -0.25 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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