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Simplifying 6k2 + -1k + -3 = 0 Reorder the terms: -3 + -1k + 6k2 = 0 Solving -3 + -1k + 6k2 = 0 Solving for variable 'k'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -0.5 + -0.1666666667k + k2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + -0.1666666667k + 0.5 + k2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + -0.1666666667k + k2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + -0.1666666667k + k2 = 0 + 0.5 -0.1666666667k + k2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 -0.1666666667k + k2 = 0.5 The k term is -0.1666666667k. Take half its coefficient (-0.08333333335). Square it (0.006944444447) and add it to both sides. Add '0.006944444447' to each side of the equation. -0.1666666667k + 0.006944444447 + k2 = 0.5 + 0.006944444447 Reorder the terms: 0.006944444447 + -0.1666666667k + k2 = 0.5 + 0.006944444447 Combine like terms: 0.5 + 0.006944444447 = 0.506944444447 0.006944444447 + -0.1666666667k + k2 = 0.506944444447 Factor a perfect square on the left side: (k + -0.08333333335)(k + -0.08333333335) = 0.506944444447 Calculate the square root of the right side: 0.712000312 Break this problem into two subproblems by setting (k + -0.08333333335) equal to 0.712000312 and -0.712000312.Subproblem 1
k + -0.08333333335 = 0.712000312 Simplifying k + -0.08333333335 = 0.712000312 Reorder the terms: -0.08333333335 + k = 0.712000312 Solving -0.08333333335 + k = 0.712000312 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '0.08333333335' to each side of the equation. -0.08333333335 + 0.08333333335 + k = 0.712000312 + 0.08333333335 Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000 0.00000000000 + k = 0.712000312 + 0.08333333335 k = 0.712000312 + 0.08333333335 Combine like terms: 0.712000312 + 0.08333333335 = 0.79533364535 k = 0.79533364535 Simplifying k = 0.79533364535Subproblem 2
k + -0.08333333335 = -0.712000312 Simplifying k + -0.08333333335 = -0.712000312 Reorder the terms: -0.08333333335 + k = -0.712000312 Solving -0.08333333335 + k = -0.712000312 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '0.08333333335' to each side of the equation. -0.08333333335 + 0.08333333335 + k = -0.712000312 + 0.08333333335 Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000 0.00000000000 + k = -0.712000312 + 0.08333333335 k = -0.712000312 + 0.08333333335 Combine like terms: -0.712000312 + 0.08333333335 = -0.62866697865 k = -0.62866697865 Simplifying k = -0.62866697865Solution
The solution to the problem is based on the solutions from the subproblems. k = {0.79533364535, -0.62866697865}
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