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Simplifying 0.3k2 + -0.6k = 2.4 Reorder the terms: -0.6k + 0.3k2 = 2.4 Solving -0.6k + 0.3k2 = 2.4 Solving for variable 'k'. Reorder the terms: -2.4 + -0.6k + 0.3k2 = 2.4 + -2.4 Combine like terms: 2.4 + -2.4 = 0.0 -2.4 + -0.6k + 0.3k2 = 0.0 Begin completing the square. Divide all terms by 0.3 the coefficient of the squared term: Divide each side by '0.3'. -8 + -2k + k2 = 0 Move the constant term to the right: Add '8' to each side of the equation. -8 + -2k + 8 + k2 = 0 + 8 Reorder the terms: -8 + 8 + -2k + k2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -2k + k2 = 0 + 8 -2k + k2 = 0 + 8 Combine like terms: 0 + 8 = 8 -2k + k2 = 8 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 = 8 + 1 Reorder the terms: 1 + -2k + k2 = 8 + 1 Combine like terms: 8 + 1 = 9 1 + -2k + k2 = 9 Factor a perfect square on the left side: (k + -1)(k + -1) = 9 Calculate the square root of the right side: 3 Break this problem into two subproblems by setting (k + -1) equal to 3 and -3.Subproblem 1
k + -1 = 3 Simplifying k + -1 = 3 Reorder the terms: -1 + k = 3 Solving -1 + k = 3 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 = 3 + 1 Combine like terms: -1 + 1 = 0 0 + k = 3 + 1 k = 3 + 1 Combine like terms: 3 + 1 = 4 k = 4 Simplifying k = 4Subproblem 2
k + -1 = -3 Simplifying k + -1 = -3 Reorder the terms: -1 + k = -3 Solving -1 + k = -3 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 = -3 + 1 Combine like terms: -1 + 1 = 0 0 + k = -3 + 1 k = -3 + 1 Combine like terms: -3 + 1 = -2 k = -2 Simplifying k = -2Solution
The solution to the problem is based on the solutions from the subproblems. k = {4, -2}
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