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Simplifying (2k2) + -12 = 12k Reorder the terms: -12 + (2k2) = 12k Solving -12 + (2k2) = 12k Solving for variable 'k'. Reorder the terms: -12 + -12k + (2k2) = 12k + -12k Combine like terms: 12k + -12k = 0 -12 + -12k + (2k2) = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-6 + -6k + k2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-6 + -6k + k2)' equal to zero and attempt to solve: Simplifying -6 + -6k + k2 = 0 Solving -6 + -6k + k2 = 0 Begin completing the square. Move the constant term to the right: Add '6' to each side of the equation. -6 + -6k + 6 + k2 = 0 + 6 Reorder the terms: -6 + 6 + -6k + k2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -6k + k2 = 0 + 6 -6k + k2 = 0 + 6 Combine like terms: 0 + 6 = 6 -6k + k2 = 6 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 = 6 + 9 Reorder the terms: 9 + -6k + k2 = 6 + 9 Combine like terms: 6 + 9 = 15 9 + -6k + k2 = 15 Factor a perfect square on the left side: (k + -3)(k + -3) = 15 Calculate the square root of the right side: 3.872983346 Break this problem into two subproblems by setting (k + -3) equal to 3.872983346 and -3.872983346.Subproblem 1
k + -3 = 3.872983346 Simplifying k + -3 = 3.872983346 Reorder the terms: -3 + k = 3.872983346 Solving -3 + k = 3.872983346 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 = 3.872983346 + 3 Combine like terms: -3 + 3 = 0 0 + k = 3.872983346 + 3 k = 3.872983346 + 3 Combine like terms: 3.872983346 + 3 = 6.872983346 k = 6.872983346 Simplifying k = 6.872983346Subproblem 2
k + -3 = -3.872983346 Simplifying k + -3 = -3.872983346 Reorder the terms: -3 + k = -3.872983346 Solving -3 + k = -3.872983346 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 = -3.872983346 + 3 Combine like terms: -3 + 3 = 0 0 + k = -3.872983346 + 3 k = -3.872983346 + 3 Combine like terms: -3.872983346 + 3 = -0.872983346 k = -0.872983346 Simplifying k = -0.872983346Solution
The solution to the problem is based on the solutions from the subproblems. k = {6.872983346, -0.872983346}Solution
k = {6.872983346, -0.872983346}
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