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Simplifying -2k2 + 3k + 8 = 0 Reorder the terms: 8 + 3k + -2k2 = 0 Solving 8 + 3k + -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'. -4 + -1.5k + k2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + -1.5k + 4 + k2 = 0 + 4 Reorder the terms: -4 + 4 + -1.5k + k2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1.5k + k2 = 0 + 4 -1.5k + k2 = 0 + 4 Combine like terms: 0 + 4 = 4 -1.5k + k2 = 4 The k term is -1.5k. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5k + 0.5625 + k2 = 4 + 0.5625 Reorder the terms: 0.5625 + -1.5k + k2 = 4 + 0.5625 Combine like terms: 4 + 0.5625 = 4.5625 0.5625 + -1.5k + k2 = 4.5625 Factor a perfect square on the left side: (k + -0.75)(k + -0.75) = 4.5625 Calculate the square root of the right side: 2.136000936 Break this problem into two subproblems by setting (k + -0.75) equal to 2.136000936 and -2.136000936.Subproblem 1
k + -0.75 = 2.136000936 Simplifying k + -0.75 = 2.136000936 Reorder the terms: -0.75 + k = 2.136000936 Solving -0.75 + k = 2.136000936 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + k = 2.136000936 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + k = 2.136000936 + 0.75 k = 2.136000936 + 0.75 Combine like terms: 2.136000936 + 0.75 = 2.886000936 k = 2.886000936 Simplifying k = 2.886000936Subproblem 2
k + -0.75 = -2.136000936 Simplifying k + -0.75 = -2.136000936 Reorder the terms: -0.75 + k = -2.136000936 Solving -0.75 + k = -2.136000936 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + k = -2.136000936 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + k = -2.136000936 + 0.75 k = -2.136000936 + 0.75 Combine like terms: -2.136000936 + 0.75 = -1.386000936 k = -1.386000936 Simplifying k = -1.386000936Solution
The solution to the problem is based on the solutions from the subproblems. k = {2.886000936, -1.386000936}
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