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Simplifying k2 + -9 = 12k Reorder the terms: -9 + k2 = 12k Solving -9 + k2 = 12k Solving for variable 'k'. Reorder the terms: -9 + -12k + k2 = 12k + -12k Combine like terms: 12k + -12k = 0 -9 + -12k + k2 = 0 Begin completing the square. Move the constant term to the right: Add '9' to each side of the equation. -9 + -12k + 9 + k2 = 0 + 9 Reorder the terms: -9 + 9 + -12k + k2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -12k + k2 = 0 + 9 -12k + k2 = 0 + 9 Combine like terms: 0 + 9 = 9 -12k + k2 = 9 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 = 9 + 36 Reorder the terms: 36 + -12k + k2 = 9 + 36 Combine like terms: 9 + 36 = 45 36 + -12k + k2 = 45 Factor a perfect square on the left side: (k + -6)(k + -6) = 45 Calculate the square root of the right side: 6.708203933 Break this problem into two subproblems by setting (k + -6) equal to 6.708203933 and -6.708203933.Subproblem 1
k + -6 = 6.708203933 Simplifying k + -6 = 6.708203933 Reorder the terms: -6 + k = 6.708203933 Solving -6 + k = 6.708203933 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 = 6.708203933 + 6 Combine like terms: -6 + 6 = 0 0 + k = 6.708203933 + 6 k = 6.708203933 + 6 Combine like terms: 6.708203933 + 6 = 12.708203933 k = 12.708203933 Simplifying k = 12.708203933Subproblem 2
k + -6 = -6.708203933 Simplifying k + -6 = -6.708203933 Reorder the terms: -6 + k = -6.708203933 Solving -6 + k = -6.708203933 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 = -6.708203933 + 6 Combine like terms: -6 + 6 = 0 0 + k = -6.708203933 + 6 k = -6.708203933 + 6 Combine like terms: -6.708203933 + 6 = -0.708203933 k = -0.708203933 Simplifying k = -0.708203933Solution
The solution to the problem is based on the solutions from the subproblems. k = {12.708203933, -0.708203933}
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