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Simplifying -10k2 + 6k + -9 = -3 Reorder the terms: -9 + 6k + -10k2 = -3 Solving -9 + 6k + -10k2 = -3 Solving for variable 'k'. Reorder the terms: -9 + 3 + 6k + -10k2 = -3 + 3 Combine like terms: -9 + 3 = -6 -6 + 6k + -10k2 = -3 + 3 Combine like terms: -3 + 3 = 0 -6 + 6k + -10k2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-3 + 3k + -5k2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-3 + 3k + -5k2)' equal to zero and attempt to solve: Simplifying -3 + 3k + -5k2 = 0 Solving -3 + 3k + -5k2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. 0.6 + -0.6k + k2 = 0 Move the constant term to the right: Add '-0.6' to each side of the equation. 0.6 + -0.6k + -0.6 + k2 = 0 + -0.6 Reorder the terms: 0.6 + -0.6 + -0.6k + k2 = 0 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + -0.6k + k2 = 0 + -0.6 -0.6k + k2 = 0 + -0.6 Combine like terms: 0 + -0.6 = -0.6 -0.6k + k2 = -0.6 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 = -0.6 + 0.09 Reorder the terms: 0.09 + -0.6k + k2 = -0.6 + 0.09 Combine like terms: -0.6 + 0.09 = -0.51 0.09 + -0.6k + k2 = -0.51 Factor a perfect square on the left side: (k + -0.3)(k + -0.3) = -0.51 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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