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Simplifying k2 + -31 + -2k + 6 + -3k2 = 0 Reorder the terms: -31 + 6 + -2k + k2 + -3k2 = 0 Combine like terms: -31 + 6 = -25 -25 + -2k + k2 + -3k2 = 0 Combine like terms: k2 + -3k2 = -2k2 -25 + -2k + -2k2 = 0 Solving -25 + -2k + -2k2 = 0 Solving for variable 'k'. Factor out the Greatest Common Factor (GCF), '-1'. -1(25 + 2k + 2k2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(25 + 2k + 2k2)' equal to zero and attempt to solve: Simplifying 25 + 2k + 2k2 = 0 Solving 25 + 2k + 2k2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 12.5 + k + k2 = 0 Move the constant term to the right: Add '-12.5' to each side of the equation. 12.5 + k + -12.5 + k2 = 0 + -12.5 Reorder the terms: 12.5 + -12.5 + k + k2 = 0 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + k + k2 = 0 + -12.5 k + k2 = 0 + -12.5 Combine like terms: 0 + -12.5 = -12.5 k + k2 = -12.5 The k term is k. 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. + 0.25 + k2 = -12.5 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + k2 = -12.5 + 0.25 Combine like terms: -12.5 + 0.25 = -12.25 1.25 + k2 = -12.25 Factor a perfect square on the left side: (k + 0.5)(k + 0.5) = -12.25 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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