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Simplifying k2 + -22k + 36 = 0 Reorder the terms: 36 + -22k + k2 = 0 Solving 36 + -22k + k2 = 0 Solving for variable 'k'. Begin completing the square. Move the constant term to the right: Add '-36' to each side of the equation. 36 + -22k + -36 + k2 = 0 + -36 Reorder the terms: 36 + -36 + -22k + k2 = 0 + -36 Combine like terms: 36 + -36 = 0 0 + -22k + k2 = 0 + -36 -22k + k2 = 0 + -36 Combine like terms: 0 + -36 = -36 -22k + k2 = -36 The k term is -22k. Take half its coefficient (-11). Square it (121) and add it to both sides. Add '121' to each side of the equation. -22k + 121 + k2 = -36 + 121 Reorder the terms: 121 + -22k + k2 = -36 + 121 Combine like terms: -36 + 121 = 85 121 + -22k + k2 = 85 Factor a perfect square on the left side: (k + -11)(k + -11) = 85 Calculate the square root of the right side: 9.219544457 Break this problem into two subproblems by setting (k + -11) equal to 9.219544457 and -9.219544457.Subproblem 1
k + -11 = 9.219544457 Simplifying k + -11 = 9.219544457 Reorder the terms: -11 + k = 9.219544457 Solving -11 + k = 9.219544457 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + k = 9.219544457 + 11 Combine like terms: -11 + 11 = 0 0 + k = 9.219544457 + 11 k = 9.219544457 + 11 Combine like terms: 9.219544457 + 11 = 20.219544457 k = 20.219544457 Simplifying k = 20.219544457Subproblem 2
k + -11 = -9.219544457 Simplifying k + -11 = -9.219544457 Reorder the terms: -11 + k = -9.219544457 Solving -11 + k = -9.219544457 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + k = -9.219544457 + 11 Combine like terms: -11 + 11 = 0 0 + k = -9.219544457 + 11 k = -9.219544457 + 11 Combine like terms: -9.219544457 + 11 = 1.780455543 k = 1.780455543 Simplifying k = 1.780455543Solution
The solution to the problem is based on the solutions from the subproblems. k = {20.219544457, 1.780455543}
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