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Simplifying k2 + 72k + 21 = 0 Reorder the terms: 21 + 72k + k2 = 0 Solving 21 + 72k + k2 = 0 Solving for variable 'k'. Begin completing the square. Move the constant term to the right: Add '-21' to each side of the equation. 21 + 72k + -21 + k2 = 0 + -21 Reorder the terms: 21 + -21 + 72k + k2 = 0 + -21 Combine like terms: 21 + -21 = 0 0 + 72k + k2 = 0 + -21 72k + k2 = 0 + -21 Combine like terms: 0 + -21 = -21 72k + k2 = -21 The k term is 72k. Take half its coefficient (36). Square it (1296) and add it to both sides. Add '1296' to each side of the equation. 72k + 1296 + k2 = -21 + 1296 Reorder the terms: 1296 + 72k + k2 = -21 + 1296 Combine like terms: -21 + 1296 = 1275 1296 + 72k + k2 = 1275 Factor a perfect square on the left side: (k + 36)(k + 36) = 1275 Calculate the square root of the right side: 35.707142143 Break this problem into two subproblems by setting (k + 36) equal to 35.707142143 and -35.707142143.Subproblem 1
k + 36 = 35.707142143 Simplifying k + 36 = 35.707142143 Reorder the terms: 36 + k = 35.707142143 Solving 36 + k = 35.707142143 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-36' to each side of the equation. 36 + -36 + k = 35.707142143 + -36 Combine like terms: 36 + -36 = 0 0 + k = 35.707142143 + -36 k = 35.707142143 + -36 Combine like terms: 35.707142143 + -36 = -0.292857857 k = -0.292857857 Simplifying k = -0.292857857Subproblem 2
k + 36 = -35.707142143 Simplifying k + 36 = -35.707142143 Reorder the terms: 36 + k = -35.707142143 Solving 36 + k = -35.707142143 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-36' to each side of the equation. 36 + -36 + k = -35.707142143 + -36 Combine like terms: 36 + -36 = 0 0 + k = -35.707142143 + -36 k = -35.707142143 + -36 Combine like terms: -35.707142143 + -36 = -71.707142143 k = -71.707142143 Simplifying k = -71.707142143Solution
The solution to the problem is based on the solutions from the subproblems. k = {-0.292857857, -71.707142143}
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