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Simplifying 2k2 + -19k + 10 = 0 Reorder the terms: 10 + -19k + 2k2 = 0 Solving 10 + -19k + 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'. 5 + -9.5k + k2 = 0 Move the constant term to the right: Add '-5' to each side of the equation. 5 + -9.5k + -5 + k2 = 0 + -5 Reorder the terms: 5 + -5 + -9.5k + k2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -9.5k + k2 = 0 + -5 -9.5k + k2 = 0 + -5 Combine like terms: 0 + -5 = -5 -9.5k + k2 = -5 The k term is -9.5k. Take half its coefficient (-4.75). Square it (22.5625) and add it to both sides. Add '22.5625' to each side of the equation. -9.5k + 22.5625 + k2 = -5 + 22.5625 Reorder the terms: 22.5625 + -9.5k + k2 = -5 + 22.5625 Combine like terms: -5 + 22.5625 = 17.5625 22.5625 + -9.5k + k2 = 17.5625 Factor a perfect square on the left side: (k + -4.75)(k + -4.75) = 17.5625 Calculate the square root of the right side: 4.190763654 Break this problem into two subproblems by setting (k + -4.75) equal to 4.190763654 and -4.190763654.Subproblem 1
k + -4.75 = 4.190763654 Simplifying k + -4.75 = 4.190763654 Reorder the terms: -4.75 + k = 4.190763654 Solving -4.75 + k = 4.190763654 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '4.75' to each side of the equation. -4.75 + 4.75 + k = 4.190763654 + 4.75 Combine like terms: -4.75 + 4.75 = 0.00 0.00 + k = 4.190763654 + 4.75 k = 4.190763654 + 4.75 Combine like terms: 4.190763654 + 4.75 = 8.940763654 k = 8.940763654 Simplifying k = 8.940763654Subproblem 2
k + -4.75 = -4.190763654 Simplifying k + -4.75 = -4.190763654 Reorder the terms: -4.75 + k = -4.190763654 Solving -4.75 + k = -4.190763654 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '4.75' to each side of the equation. -4.75 + 4.75 + k = -4.190763654 + 4.75 Combine like terms: -4.75 + 4.75 = 0.00 0.00 + k = -4.190763654 + 4.75 k = -4.190763654 + 4.75 Combine like terms: -4.190763654 + 4.75 = 0.559236346 k = 0.559236346 Simplifying k = 0.559236346Solution
The solution to the problem is based on the solutions from the subproblems. k = {8.940763654, 0.559236346}
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