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Simplifying 2k2 + 72 = 33k Reorder the terms: 72 + 2k2 = 33k Solving 72 + 2k2 = 33k Solving for variable 'k'. Reorder the terms: 72 + -33k + 2k2 = 33k + -33k Combine like terms: 33k + -33k = 0 72 + -33k + 2k2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 36 + -16.5k + k2 = 0 Move the constant term to the right: Add '-36' to each side of the equation. 36 + -16.5k + -36 + k2 = 0 + -36 Reorder the terms: 36 + -36 + -16.5k + k2 = 0 + -36 Combine like terms: 36 + -36 = 0 0 + -16.5k + k2 = 0 + -36 -16.5k + k2 = 0 + -36 Combine like terms: 0 + -36 = -36 -16.5k + k2 = -36 The k term is -16.5k. Take half its coefficient (-8.25). Square it (68.0625) and add it to both sides. Add '68.0625' to each side of the equation. -16.5k + 68.0625 + k2 = -36 + 68.0625 Reorder the terms: 68.0625 + -16.5k + k2 = -36 + 68.0625 Combine like terms: -36 + 68.0625 = 32.0625 68.0625 + -16.5k + k2 = 32.0625 Factor a perfect square on the left side: (k + -8.25)(k + -8.25) = 32.0625 Calculate the square root of the right side: 5.662375826 Break this problem into two subproblems by setting (k + -8.25) equal to 5.662375826 and -5.662375826.Subproblem 1
k + -8.25 = 5.662375826 Simplifying k + -8.25 = 5.662375826 Reorder the terms: -8.25 + k = 5.662375826 Solving -8.25 + k = 5.662375826 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '8.25' to each side of the equation. -8.25 + 8.25 + k = 5.662375826 + 8.25 Combine like terms: -8.25 + 8.25 = 0.00 0.00 + k = 5.662375826 + 8.25 k = 5.662375826 + 8.25 Combine like terms: 5.662375826 + 8.25 = 13.912375826 k = 13.912375826 Simplifying k = 13.912375826Subproblem 2
k + -8.25 = -5.662375826 Simplifying k + -8.25 = -5.662375826 Reorder the terms: -8.25 + k = -5.662375826 Solving -8.25 + k = -5.662375826 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '8.25' to each side of the equation. -8.25 + 8.25 + k = -5.662375826 + 8.25 Combine like terms: -8.25 + 8.25 = 0.00 0.00 + k = -5.662375826 + 8.25 k = -5.662375826 + 8.25 Combine like terms: -5.662375826 + 8.25 = 2.587624174 k = 2.587624174 Simplifying k = 2.587624174Solution
The solution to the problem is based on the solutions from the subproblems. k = {13.912375826, 2.587624174}
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