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Simplifying k2 + -18k + 37 = 8 Reorder the terms: 37 + -18k + k2 = 8 Solving 37 + -18k + k2 = 8 Solving for variable 'k'. Reorder the terms: 37 + -8 + -18k + k2 = 8 + -8 Combine like terms: 37 + -8 = 29 29 + -18k + k2 = 8 + -8 Combine like terms: 8 + -8 = 0 29 + -18k + k2 = 0 Begin completing the square. Move the constant term to the right: Add '-29' to each side of the equation. 29 + -18k + -29 + k2 = 0 + -29 Reorder the terms: 29 + -29 + -18k + k2 = 0 + -29 Combine like terms: 29 + -29 = 0 0 + -18k + k2 = 0 + -29 -18k + k2 = 0 + -29 Combine like terms: 0 + -29 = -29 -18k + k2 = -29 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 = -29 + 81 Reorder the terms: 81 + -18k + k2 = -29 + 81 Combine like terms: -29 + 81 = 52 81 + -18k + k2 = 52 Factor a perfect square on the left side: (k + -9)(k + -9) = 52 Calculate the square root of the right side: 7.211102551 Break this problem into two subproblems by setting (k + -9) equal to 7.211102551 and -7.211102551.Subproblem 1
k + -9 = 7.211102551 Simplifying k + -9 = 7.211102551 Reorder the terms: -9 + k = 7.211102551 Solving -9 + k = 7.211102551 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 = 7.211102551 + 9 Combine like terms: -9 + 9 = 0 0 + k = 7.211102551 + 9 k = 7.211102551 + 9 Combine like terms: 7.211102551 + 9 = 16.211102551 k = 16.211102551 Simplifying k = 16.211102551Subproblem 2
k + -9 = -7.211102551 Simplifying k + -9 = -7.211102551 Reorder the terms: -9 + k = -7.211102551 Solving -9 + k = -7.211102551 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 = -7.211102551 + 9 Combine like terms: -9 + 9 = 0 0 + k = -7.211102551 + 9 k = -7.211102551 + 9 Combine like terms: -7.211102551 + 9 = 1.788897449 k = 1.788897449 Simplifying k = 1.788897449Solution
The solution to the problem is based on the solutions from the subproblems. k = {16.211102551, 1.788897449}
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