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Simplifying k2 + 30k = -37 Reorder the terms: 30k + k2 = -37 Solving 30k + k2 = -37 Solving for variable 'k'. Reorder the terms: 37 + 30k + k2 = -37 + 37 Combine like terms: -37 + 37 = 0 37 + 30k + k2 = 0 Begin completing the square. Move the constant term to the right: Add '-37' to each side of the equation. 37 + 30k + -37 + k2 = 0 + -37 Reorder the terms: 37 + -37 + 30k + k2 = 0 + -37 Combine like terms: 37 + -37 = 0 0 + 30k + k2 = 0 + -37 30k + k2 = 0 + -37 Combine like terms: 0 + -37 = -37 30k + k2 = -37 The k term is 30k. Take half its coefficient (15). Square it (225) and add it to both sides. Add '225' to each side of the equation. 30k + 225 + k2 = -37 + 225 Reorder the terms: 225 + 30k + k2 = -37 + 225 Combine like terms: -37 + 225 = 188 225 + 30k + k2 = 188 Factor a perfect square on the left side: (k + 15)(k + 15) = 188 Calculate the square root of the right side: 13.711309201 Break this problem into two subproblems by setting (k + 15) equal to 13.711309201 and -13.711309201.Subproblem 1
k + 15 = 13.711309201 Simplifying k + 15 = 13.711309201 Reorder the terms: 15 + k = 13.711309201 Solving 15 + k = 13.711309201 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + k = 13.711309201 + -15 Combine like terms: 15 + -15 = 0 0 + k = 13.711309201 + -15 k = 13.711309201 + -15 Combine like terms: 13.711309201 + -15 = -1.288690799 k = -1.288690799 Simplifying k = -1.288690799Subproblem 2
k + 15 = -13.711309201 Simplifying k + 15 = -13.711309201 Reorder the terms: 15 + k = -13.711309201 Solving 15 + k = -13.711309201 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + k = -13.711309201 + -15 Combine like terms: 15 + -15 = 0 0 + k = -13.711309201 + -15 k = -13.711309201 + -15 Combine like terms: -13.711309201 + -15 = -28.711309201 k = -28.711309201 Simplifying k = -28.711309201Solution
The solution to the problem is based on the solutions from the subproblems. k = {-1.288690799, -28.711309201}
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