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Simplifying 10k2 + -6k + 18 = 0 Reorder the terms: 18 + -6k + 10k2 = 0 Solving 18 + -6k + 10k2 = 0 Solving for variable 'k'. Factor out the Greatest Common Factor (GCF), '2'. 2(9 + -3k + 5k2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(9 + -3k + 5k2)' equal to zero and attempt to solve: Simplifying 9 + -3k + 5k2 = 0 Solving 9 + -3k + 5k2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 1.8 + -0.6k + k2 = 0 Move the constant term to the right: Add '-1.8' to each side of the equation. 1.8 + -0.6k + -1.8 + k2 = 0 + -1.8 Reorder the terms: 1.8 + -1.8 + -0.6k + k2 = 0 + -1.8 Combine like terms: 1.8 + -1.8 = 0.0 0.0 + -0.6k + k2 = 0 + -1.8 -0.6k + k2 = 0 + -1.8 Combine like terms: 0 + -1.8 = -1.8 -0.6k + k2 = -1.8 The k term is -0.6k. Take half its coefficient (-0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. -0.6k + 0.09 + k2 = -1.8 + 0.09 Reorder the terms: 0.09 + -0.6k + k2 = -1.8 + 0.09 Combine like terms: -1.8 + 0.09 = -1.71 0.09 + -0.6k + k2 = -1.71 Factor a perfect square on the left side: (k + -0.3)(k + -0.3) = -1.71 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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