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Simplifying 0.3k(k + -0.2) = 0.6 Reorder the terms: 0.3k(-0.2 + k) = 0.6 (-0.2 * 0.3k + k * 0.3k) = 0.6 (-0.06k + 0.3k2) = 0.6 Solving -0.06k + 0.3k2 = 0.6 Solving for variable 'k'. Reorder the terms: -0.6 + -0.06k + 0.3k2 = 0.6 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 -0.6 + -0.06k + 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'. -2 + -0.2k + k2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -0.2k + 2 + k2 = 0 + 2 Reorder the terms: -2 + 2 + -0.2k + k2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -0.2k + k2 = 0 + 2 -0.2k + k2 = 0 + 2 Combine like terms: 0 + 2 = 2 -0.2k + k2 = 2 The k term is -0.2k. Take half its coefficient (-0.1). Square it (0.01) and add it to both sides. Add '0.01' to each side of the equation. -0.2k + 0.01 + k2 = 2 + 0.01 Reorder the terms: 0.01 + -0.2k + k2 = 2 + 0.01 Combine like terms: 2 + 0.01 = 2.01 0.01 + -0.2k + k2 = 2.01 Factor a perfect square on the left side: (k + -0.1)(k + -0.1) = 2.01 Calculate the square root of the right side: 1.417744688 Break this problem into two subproblems by setting (k + -0.1) equal to 1.417744688 and -1.417744688.Subproblem 1
k + -0.1 = 1.417744688 Simplifying k + -0.1 = 1.417744688 Reorder the terms: -0.1 + k = 1.417744688 Solving -0.1 + k = 1.417744688 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '0.1' to each side of the equation. -0.1 + 0.1 + k = 1.417744688 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + k = 1.417744688 + 0.1 k = 1.417744688 + 0.1 Combine like terms: 1.417744688 + 0.1 = 1.517744688 k = 1.517744688 Simplifying k = 1.517744688Subproblem 2
k + -0.1 = -1.417744688 Simplifying k + -0.1 = -1.417744688 Reorder the terms: -0.1 + k = -1.417744688 Solving -0.1 + k = -1.417744688 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '0.1' to each side of the equation. -0.1 + 0.1 + k = -1.417744688 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + k = -1.417744688 + 0.1 k = -1.417744688 + 0.1 Combine like terms: -1.417744688 + 0.1 = -1.317744688 k = -1.317744688 Simplifying k = -1.317744688Solution
The solution to the problem is based on the solutions from the subproblems. k = {1.517744688, -1.317744688}
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