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Simplifying k2 + 6k + -36 = 0 Reorder the terms: -36 + 6k + k2 = 0 Solving -36 + 6k + 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 + 6k + 36 + k2 = 0 + 36 Reorder the terms: -36 + 36 + 6k + k2 = 0 + 36 Combine like terms: -36 + 36 = 0 0 + 6k + k2 = 0 + 36 6k + k2 = 0 + 36 Combine like terms: 0 + 36 = 36 6k + k2 = 36 The k term is 6k. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6k + 9 + k2 = 36 + 9 Reorder the terms: 9 + 6k + k2 = 36 + 9 Combine like terms: 36 + 9 = 45 9 + 6k + k2 = 45 Factor a perfect square on the left side: (k + 3)(k + 3) = 45 Calculate the square root of the right side: 6.708203933 Break this problem into two subproblems by setting (k + 3) equal to 6.708203933 and -6.708203933.Subproblem 1
k + 3 = 6.708203933 Simplifying k + 3 = 6.708203933 Reorder the terms: 3 + k = 6.708203933 Solving 3 + k = 6.708203933 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + k = 6.708203933 + -3 Combine like terms: 3 + -3 = 0 0 + k = 6.708203933 + -3 k = 6.708203933 + -3 Combine like terms: 6.708203933 + -3 = 3.708203933 k = 3.708203933 Simplifying k = 3.708203933Subproblem 2
k + 3 = -6.708203933 Simplifying k + 3 = -6.708203933 Reorder the terms: 3 + k = -6.708203933 Solving 3 + k = -6.708203933 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + k = -6.708203933 + -3 Combine like terms: 3 + -3 = 0 0 + k = -6.708203933 + -3 k = -6.708203933 + -3 Combine like terms: -6.708203933 + -3 = -9.708203933 k = -9.708203933 Simplifying k = -9.708203933Solution
The solution to the problem is based on the solutions from the subproblems. k = {3.708203933, -9.708203933}
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