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Simplifying -6k2 + 3k + 2 = 0 Reorder the terms: 2 + 3k + -6k2 = 0 Solving 2 + 3k + -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'. -0.3333333333 + -0.5k + k2 = 0 Move the constant term to the right: Add '0.3333333333' to each side of the equation. -0.3333333333 + -0.5k + 0.3333333333 + k2 = 0 + 0.3333333333 Reorder the terms: -0.3333333333 + 0.3333333333 + -0.5k + k2 = 0 + 0.3333333333 Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000 0.0000000000 + -0.5k + k2 = 0 + 0.3333333333 -0.5k + k2 = 0 + 0.3333333333 Combine like terms: 0 + 0.3333333333 = 0.3333333333 -0.5k + k2 = 0.3333333333 The k term is -0.5k. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5k + 0.0625 + k2 = 0.3333333333 + 0.0625 Reorder the terms: 0.0625 + -0.5k + k2 = 0.3333333333 + 0.0625 Combine like terms: 0.3333333333 + 0.0625 = 0.3958333333 0.0625 + -0.5k + k2 = 0.3958333333 Factor a perfect square on the left side: (k + -0.25)(k + -0.25) = 0.3958333333 Calculate the square root of the right side: 0.62915287 Break this problem into two subproblems by setting (k + -0.25) equal to 0.62915287 and -0.62915287.Subproblem 1
k + -0.25 = 0.62915287 Simplifying k + -0.25 = 0.62915287 Reorder the terms: -0.25 + k = 0.62915287 Solving -0.25 + k = 0.62915287 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + k = 0.62915287 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + k = 0.62915287 + 0.25 k = 0.62915287 + 0.25 Combine like terms: 0.62915287 + 0.25 = 0.87915287 k = 0.87915287 Simplifying k = 0.87915287Subproblem 2
k + -0.25 = -0.62915287 Simplifying k + -0.25 = -0.62915287 Reorder the terms: -0.25 + k = -0.62915287 Solving -0.25 + k = -0.62915287 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + k = -0.62915287 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + k = -0.62915287 + 0.25 k = -0.62915287 + 0.25 Combine like terms: -0.62915287 + 0.25 = -0.37915287 k = -0.37915287 Simplifying k = -0.37915287Solution
The solution to the problem is based on the solutions from the subproblems. k = {0.87915287, -0.37915287}
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