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Simplifying 12k2 + -4 = 7k Reorder the terms: -4 + 12k2 = 7k Solving -4 + 12k2 = 7k Solving for variable 'k'. Reorder the terms: -4 + -7k + 12k2 = 7k + -7k Combine like terms: 7k + -7k = 0 -4 + -7k + 12k2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -0.3333333333 + -0.5833333333k + k2 = 0 Move the constant term to the right: Add '0.3333333333' to each side of the equation. -0.3333333333 + -0.5833333333k + 0.3333333333 + k2 = 0 + 0.3333333333 Reorder the terms: -0.3333333333 + 0.3333333333 + -0.5833333333k + k2 = 0 + 0.3333333333 Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000 0.0000000000 + -0.5833333333k + k2 = 0 + 0.3333333333 -0.5833333333k + k2 = 0 + 0.3333333333 Combine like terms: 0 + 0.3333333333 = 0.3333333333 -0.5833333333k + k2 = 0.3333333333 The k term is -0.5833333333k. Take half its coefficient (-0.2916666667). Square it (0.08506944446) and add it to both sides. Add '0.08506944446' to each side of the equation. -0.5833333333k + 0.08506944446 + k2 = 0.3333333333 + 0.08506944446 Reorder the terms: 0.08506944446 + -0.5833333333k + k2 = 0.3333333333 + 0.08506944446 Combine like terms: 0.3333333333 + 0.08506944446 = 0.41840277776 0.08506944446 + -0.5833333333k + k2 = 0.41840277776 Factor a perfect square on the left side: (k + -0.2916666667)(k + -0.2916666667) = 0.41840277776 Calculate the square root of the right side: 0.646840612 Break this problem into two subproblems by setting (k + -0.2916666667) equal to 0.646840612 and -0.646840612.Subproblem 1
k + -0.2916666667 = 0.646840612 Simplifying k + -0.2916666667 = 0.646840612 Reorder the terms: -0.2916666667 + k = 0.646840612 Solving -0.2916666667 + k = 0.646840612 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '0.2916666667' to each side of the equation. -0.2916666667 + 0.2916666667 + k = 0.646840612 + 0.2916666667 Combine like terms: -0.2916666667 + 0.2916666667 = 0.0000000000 0.0000000000 + k = 0.646840612 + 0.2916666667 k = 0.646840612 + 0.2916666667 Combine like terms: 0.646840612 + 0.2916666667 = 0.9385072787 k = 0.9385072787 Simplifying k = 0.9385072787Subproblem 2
k + -0.2916666667 = -0.646840612 Simplifying k + -0.2916666667 = -0.646840612 Reorder the terms: -0.2916666667 + k = -0.646840612 Solving -0.2916666667 + k = -0.646840612 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '0.2916666667' to each side of the equation. -0.2916666667 + 0.2916666667 + k = -0.646840612 + 0.2916666667 Combine like terms: -0.2916666667 + 0.2916666667 = 0.0000000000 0.0000000000 + k = -0.646840612 + 0.2916666667 k = -0.646840612 + 0.2916666667 Combine like terms: -0.646840612 + 0.2916666667 = -0.3551739453 k = -0.3551739453 Simplifying k = -0.3551739453Solution
The solution to the problem is based on the solutions from the subproblems. k = {0.9385072787, -0.3551739453}
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