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Simplifying 3k2 + 6k = 10 Reorder the terms: 6k + 3k2 = 10 Solving 6k + 3k2 = 10 Solving for variable 'k'. Reorder the terms: -10 + 6k + 3k2 = 10 + -10 Combine like terms: 10 + -10 = 0 -10 + 6k + 3k2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -3.333333333 + 2k + k2 = 0 Move the constant term to the right: Add '3.333333333' to each side of the equation. -3.333333333 + 2k + 3.333333333 + k2 = 0 + 3.333333333 Reorder the terms: -3.333333333 + 3.333333333 + 2k + k2 = 0 + 3.333333333 Combine like terms: -3.333333333 + 3.333333333 = 0.000000000 0.000000000 + 2k + k2 = 0 + 3.333333333 2k + k2 = 0 + 3.333333333 Combine like terms: 0 + 3.333333333 = 3.333333333 2k + k2 = 3.333333333 The k term is 2k. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2k + 1 + k2 = 3.333333333 + 1 Reorder the terms: 1 + 2k + k2 = 3.333333333 + 1 Combine like terms: 3.333333333 + 1 = 4.333333333 1 + 2k + k2 = 4.333333333 Factor a perfect square on the left side: (k + 1)(k + 1) = 4.333333333 Calculate the square root of the right side: 2.081665999 Break this problem into two subproblems by setting (k + 1) equal to 2.081665999 and -2.081665999.Subproblem 1
k + 1 = 2.081665999 Simplifying k + 1 = 2.081665999 Reorder the terms: 1 + k = 2.081665999 Solving 1 + k = 2.081665999 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + k = 2.081665999 + -1 Combine like terms: 1 + -1 = 0 0 + k = 2.081665999 + -1 k = 2.081665999 + -1 Combine like terms: 2.081665999 + -1 = 1.081665999 k = 1.081665999 Simplifying k = 1.081665999Subproblem 2
k + 1 = -2.081665999 Simplifying k + 1 = -2.081665999 Reorder the terms: 1 + k = -2.081665999 Solving 1 + k = -2.081665999 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + k = -2.081665999 + -1 Combine like terms: 1 + -1 = 0 0 + k = -2.081665999 + -1 k = -2.081665999 + -1 Combine like terms: -2.081665999 + -1 = -3.081665999 k = -3.081665999 Simplifying k = -3.081665999Solution
The solution to the problem is based on the solutions from the subproblems. k = {1.081665999, -3.081665999}
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