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Simplifying 2k2 + -1k + -6.25 = 0 Reorder the terms: -6.25 + -1k + 2k2 = 0 Solving -6.25 + -1k + 2k2 = 0 Solving for variable 'k'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -3.125 + -0.5k + k2 = 0 Move the constant term to the right: Add '3.125' to each side of the equation. -3.125 + -0.5k + 3.125 + k2 = 0 + 3.125 Reorder the terms: -3.125 + 3.125 + -0.5k + k2 = 0 + 3.125 Combine like terms: -3.125 + 3.125 = 0.000 0.000 + -0.5k + k2 = 0 + 3.125 -0.5k + k2 = 0 + 3.125 Combine like terms: 0 + 3.125 = 3.125 -0.5k + k2 = 3.125 The k term is -0.5k. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5k + 0.0625 + k2 = 3.125 + 0.0625 Reorder the terms: 0.0625 + -0.5k + k2 = 3.125 + 0.0625 Combine like terms: 3.125 + 0.0625 = 3.1875 0.0625 + -0.5k + k2 = 3.1875 Factor a perfect square on the left side: (k + -0.25)(k + -0.25) = 3.1875 Calculate the square root of the right side: 1.785357107 Break this problem into two subproblems by setting (k + -0.25) equal to 1.785357107 and -1.785357107.Subproblem 1
k + -0.25 = 1.785357107 Simplifying k + -0.25 = 1.785357107 Reorder the terms: -0.25 + k = 1.785357107 Solving -0.25 + k = 1.785357107 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + k = 1.785357107 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + k = 1.785357107 + 0.25 k = 1.785357107 + 0.25 Combine like terms: 1.785357107 + 0.25 = 2.035357107 k = 2.035357107 Simplifying k = 2.035357107Subproblem 2
k + -0.25 = -1.785357107 Simplifying k + -0.25 = -1.785357107 Reorder the terms: -0.25 + k = -1.785357107 Solving -0.25 + k = -1.785357107 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + k = -1.785357107 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + k = -1.785357107 + 0.25 k = -1.785357107 + 0.25 Combine like terms: -1.785357107 + 0.25 = -1.535357107 k = -1.535357107 Simplifying k = -1.535357107Solution
The solution to the problem is based on the solutions from the subproblems. k = {2.035357107, -1.535357107}
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