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Simplifying 3k2 + -12k + 2 = 0 Reorder the terms: 2 + -12k + 3k2 = 0 Solving 2 + -12k + 3k2 = 0 Solving for variable 'k'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 0.6666666667 + -4k + k2 = 0 Move the constant term to the right: Add '-0.6666666667' to each side of the equation. 0.6666666667 + -4k + -0.6666666667 + k2 = 0 + -0.6666666667 Reorder the terms: 0.6666666667 + -0.6666666667 + -4k + k2 = 0 + -0.6666666667 Combine like terms: 0.6666666667 + -0.6666666667 = 0.0000000000 0.0000000000 + -4k + k2 = 0 + -0.6666666667 -4k + k2 = 0 + -0.6666666667 Combine like terms: 0 + -0.6666666667 = -0.6666666667 -4k + k2 = -0.6666666667 The k term is -4k. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4k + 4 + k2 = -0.6666666667 + 4 Reorder the terms: 4 + -4k + k2 = -0.6666666667 + 4 Combine like terms: -0.6666666667 + 4 = 3.3333333333 4 + -4k + k2 = 3.3333333333 Factor a perfect square on the left side: (k + -2)(k + -2) = 3.3333333333 Calculate the square root of the right side: 1.825741858 Break this problem into two subproblems by setting (k + -2) equal to 1.825741858 and -1.825741858.Subproblem 1
k + -2 = 1.825741858 Simplifying k + -2 = 1.825741858 Reorder the terms: -2 + k = 1.825741858 Solving -2 + k = 1.825741858 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + k = 1.825741858 + 2 Combine like terms: -2 + 2 = 0 0 + k = 1.825741858 + 2 k = 1.825741858 + 2 Combine like terms: 1.825741858 + 2 = 3.825741858 k = 3.825741858 Simplifying k = 3.825741858Subproblem 2
k + -2 = -1.825741858 Simplifying k + -2 = -1.825741858 Reorder the terms: -2 + k = -1.825741858 Solving -2 + k = -1.825741858 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + k = -1.825741858 + 2 Combine like terms: -2 + 2 = 0 0 + k = -1.825741858 + 2 k = -1.825741858 + 2 Combine like terms: -1.825741858 + 2 = 0.174258142 k = 0.174258142 Simplifying k = 0.174258142Solution
The solution to the problem is based on the solutions from the subproblems. k = {3.825741858, 0.174258142}
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