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Simplifying k2 + 12k + -19 = 0 Reorder the terms: -19 + 12k + k2 = 0 Solving -19 + 12k + k2 = 0 Solving for variable 'k'. Begin completing the square. Move the constant term to the right: Add '19' to each side of the equation. -19 + 12k + 19 + k2 = 0 + 19 Reorder the terms: -19 + 19 + 12k + k2 = 0 + 19 Combine like terms: -19 + 19 = 0 0 + 12k + k2 = 0 + 19 12k + k2 = 0 + 19 Combine like terms: 0 + 19 = 19 12k + k2 = 19 The k term is 12k. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12k + 36 + k2 = 19 + 36 Reorder the terms: 36 + 12k + k2 = 19 + 36 Combine like terms: 19 + 36 = 55 36 + 12k + k2 = 55 Factor a perfect square on the left side: (k + 6)(k + 6) = 55 Calculate the square root of the right side: 7.416198487 Break this problem into two subproblems by setting (k + 6) equal to 7.416198487 and -7.416198487.Subproblem 1
k + 6 = 7.416198487 Simplifying k + 6 = 7.416198487 Reorder the terms: 6 + k = 7.416198487 Solving 6 + k = 7.416198487 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + k = 7.416198487 + -6 Combine like terms: 6 + -6 = 0 0 + k = 7.416198487 + -6 k = 7.416198487 + -6 Combine like terms: 7.416198487 + -6 = 1.416198487 k = 1.416198487 Simplifying k = 1.416198487Subproblem 2
k + 6 = -7.416198487 Simplifying k + 6 = -7.416198487 Reorder the terms: 6 + k = -7.416198487 Solving 6 + k = -7.416198487 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + k = -7.416198487 + -6 Combine like terms: 6 + -6 = 0 0 + k = -7.416198487 + -6 k = -7.416198487 + -6 Combine like terms: -7.416198487 + -6 = -13.416198487 k = -13.416198487 Simplifying k = -13.416198487Solution
The solution to the problem is based on the solutions from the subproblems. k = {1.416198487, -13.416198487}
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