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Simplifying k2 + -18k + 50 = 0 Reorder the terms: 50 + -18k + k2 = 0 Solving 50 + -18k + k2 = 0 Solving for variable 'k'. Begin completing the square. Move the constant term to the right: Add '-50' to each side of the equation. 50 + -18k + -50 + k2 = 0 + -50 Reorder the terms: 50 + -50 + -18k + k2 = 0 + -50 Combine like terms: 50 + -50 = 0 0 + -18k + k2 = 0 + -50 -18k + k2 = 0 + -50 Combine like terms: 0 + -50 = -50 -18k + k2 = -50 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 = -50 + 81 Reorder the terms: 81 + -18k + k2 = -50 + 81 Combine like terms: -50 + 81 = 31 81 + -18k + k2 = 31 Factor a perfect square on the left side: (k + -9)(k + -9) = 31 Calculate the square root of the right side: 5.567764363 Break this problem into two subproblems by setting (k + -9) equal to 5.567764363 and -5.567764363.Subproblem 1
k + -9 = 5.567764363 Simplifying k + -9 = 5.567764363 Reorder the terms: -9 + k = 5.567764363 Solving -9 + k = 5.567764363 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 = 5.567764363 + 9 Combine like terms: -9 + 9 = 0 0 + k = 5.567764363 + 9 k = 5.567764363 + 9 Combine like terms: 5.567764363 + 9 = 14.567764363 k = 14.567764363 Simplifying k = 14.567764363Subproblem 2
k + -9 = -5.567764363 Simplifying k + -9 = -5.567764363 Reorder the terms: -9 + k = -5.567764363 Solving -9 + k = -5.567764363 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 = -5.567764363 + 9 Combine like terms: -9 + 9 = 0 0 + k = -5.567764363 + 9 k = -5.567764363 + 9 Combine like terms: -5.567764363 + 9 = 3.432235637 k = 3.432235637 Simplifying k = 3.432235637Solution
The solution to the problem is based on the solutions from the subproblems. k = {14.567764363, 3.432235637}
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