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Simplifying 0.5k2 + -2k = 1 Reorder the terms: -2k + 0.5k2 = 1 Solving -2k + 0.5k2 = 1 Solving for variable 'k'. Reorder the terms: -1 + -2k + 0.5k2 = 1 + -1 Combine like terms: 1 + -1 = 0 -1 + -2k + 0.5k2 = 0 Begin completing the square. Divide all terms by 0.5 the coefficient of the squared term: Divide each side by '0.5'. -2 + -4k + k2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -4k + 2 + k2 = 0 + 2 Reorder the terms: -2 + 2 + -4k + k2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -4k + k2 = 0 + 2 -4k + k2 = 0 + 2 Combine like terms: 0 + 2 = 2 -4k + k2 = 2 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 = 2 + 4 Reorder the terms: 4 + -4k + k2 = 2 + 4 Combine like terms: 2 + 4 = 6 4 + -4k + k2 = 6 Factor a perfect square on the left side: (k + -2)(k + -2) = 6 Calculate the square root of the right side: 2.449489743 Break this problem into two subproblems by setting (k + -2) equal to 2.449489743 and -2.449489743.Subproblem 1
k + -2 = 2.449489743 Simplifying k + -2 = 2.449489743 Reorder the terms: -2 + k = 2.449489743 Solving -2 + k = 2.449489743 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 = 2.449489743 + 2 Combine like terms: -2 + 2 = 0 0 + k = 2.449489743 + 2 k = 2.449489743 + 2 Combine like terms: 2.449489743 + 2 = 4.449489743 k = 4.449489743 Simplifying k = 4.449489743Subproblem 2
k + -2 = -2.449489743 Simplifying k + -2 = -2.449489743 Reorder the terms: -2 + k = -2.449489743 Solving -2 + k = -2.449489743 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 = -2.449489743 + 2 Combine like terms: -2 + 2 = 0 0 + k = -2.449489743 + 2 k = -2.449489743 + 2 Combine like terms: -2.449489743 + 2 = -0.449489743 k = -0.449489743 Simplifying k = -0.449489743Solution
The solution to the problem is based on the solutions from the subproblems. k = {4.449489743, -0.449489743}
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