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Simplifying -10k2 + -3k + -1 = 0 Reorder the terms: -1 + -3k + -10k2 = 0 Solving -1 + -3k + -10k2 = 0 Solving for variable 'k'. Factor out the Greatest Common Factor (GCF), '-1'. -1(1 + 3k + 10k2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(1 + 3k + 10k2)' equal to zero and attempt to solve: Simplifying 1 + 3k + 10k2 = 0 Solving 1 + 3k + 10k2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. 0.1 + 0.3k + k2 = 0.0 Move the constant term to the right: Add '-0.1' to each side of the equation. 0.1 + 0.3k + -0.1 + k2 = 0.0 + -0.1 Reorder the terms: 0.1 + -0.1 + 0.3k + k2 = 0.0 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + 0.3k + k2 = 0.0 + -0.1 0.3k + k2 = 0.0 + -0.1 Combine like terms: 0.0 + -0.1 = -0.1 0.3k + k2 = -0.1 The k term is 0.3k. Take half its coefficient (0.15). Square it (0.0225) and add it to both sides. Add '0.0225' to each side of the equation. 0.3k + 0.0225 + k2 = -0.1 + 0.0225 Reorder the terms: 0.0225 + 0.3k + k2 = -0.1 + 0.0225 Combine like terms: -0.1 + 0.0225 = -0.0775 0.0225 + 0.3k + k2 = -0.0775 Factor a perfect square on the left side: (k + 0.15)(k + 0.15) = -0.0775 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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