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Simplifying k2 = -18k + 36 Reorder the terms: k2 = 36 + -18k Solving k2 = 36 + -18k Solving for variable 'k'. Reorder the terms: -36 + 18k + k2 = 36 + -18k + -36 + 18k Reorder the terms: -36 + 18k + k2 = 36 + -36 + -18k + 18k Combine like terms: 36 + -36 = 0 -36 + 18k + k2 = 0 + -18k + 18k -36 + 18k + k2 = -18k + 18k Combine like terms: -18k + 18k = 0 -36 + 18k + k2 = 0 Begin completing the square. Move the constant term to the right: Add '36' to each side of the equation. -36 + 18k + 36 + k2 = 0 + 36 Reorder the terms: -36 + 36 + 18k + k2 = 0 + 36 Combine like terms: -36 + 36 = 0 0 + 18k + k2 = 0 + 36 18k + k2 = 0 + 36 Combine like terms: 0 + 36 = 36 18k + k2 = 36 The k term is 18k. Take half its coefficient (9). Square it (81) and add it to both sides. Add '81' to each side of the equation. 18k + 81 + k2 = 36 + 81 Reorder the terms: 81 + 18k + k2 = 36 + 81 Combine like terms: 36 + 81 = 117 81 + 18k + k2 = 117 Factor a perfect square on the left side: (k + 9)(k + 9) = 117 Calculate the square root of the right side: 10.816653826 Break this problem into two subproblems by setting (k + 9) equal to 10.816653826 and -10.816653826.Subproblem 1
k + 9 = 10.816653826 Simplifying k + 9 = 10.816653826 Reorder the terms: 9 + k = 10.816653826 Solving 9 + k = 10.816653826 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + k = 10.816653826 + -9 Combine like terms: 9 + -9 = 0 0 + k = 10.816653826 + -9 k = 10.816653826 + -9 Combine like terms: 10.816653826 + -9 = 1.816653826 k = 1.816653826 Simplifying k = 1.816653826Subproblem 2
k + 9 = -10.816653826 Simplifying k + 9 = -10.816653826 Reorder the terms: 9 + k = -10.816653826 Solving 9 + k = -10.816653826 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + k = -10.816653826 + -9 Combine like terms: 9 + -9 = 0 0 + k = -10.816653826 + -9 k = -10.816653826 + -9 Combine like terms: -10.816653826 + -9 = -19.816653826 k = -19.816653826 Simplifying k = -19.816653826Solution
The solution to the problem is based on the solutions from the subproblems. k = {1.816653826, -19.816653826}
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