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Simplifying 4k2 + -10k + -12 = 0 Reorder the terms: -12 + -10k + 4k2 = 0 Solving -12 + -10k + 4k2 = 0 Solving for variable 'k'. Factor out the Greatest Common Factor (GCF), '2'. 2(-6 + -5k + 2k2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-6 + -5k + 2k2)' equal to zero and attempt to solve: Simplifying -6 + -5k + 2k2 = 0 Solving -6 + -5k + 2k2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -3 + -2.5k + k2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + -2.5k + 3 + k2 = 0 + 3 Reorder the terms: -3 + 3 + -2.5k + k2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -2.5k + k2 = 0 + 3 -2.5k + k2 = 0 + 3 Combine like terms: 0 + 3 = 3 -2.5k + k2 = 3 The k term is -2.5k. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5k + 1.5625 + k2 = 3 + 1.5625 Reorder the terms: 1.5625 + -2.5k + k2 = 3 + 1.5625 Combine like terms: 3 + 1.5625 = 4.5625 1.5625 + -2.5k + k2 = 4.5625 Factor a perfect square on the left side: (k + -1.25)(k + -1.25) = 4.5625 Calculate the square root of the right side: 2.136000936 Break this problem into two subproblems by setting (k + -1.25) equal to 2.136000936 and -2.136000936.Subproblem 1
k + -1.25 = 2.136000936 Simplifying k + -1.25 = 2.136000936 Reorder the terms: -1.25 + k = 2.136000936 Solving -1.25 + k = 2.136000936 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + k = 2.136000936 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + k = 2.136000936 + 1.25 k = 2.136000936 + 1.25 Combine like terms: 2.136000936 + 1.25 = 3.386000936 k = 3.386000936 Simplifying k = 3.386000936Subproblem 2
k + -1.25 = -2.136000936 Simplifying k + -1.25 = -2.136000936 Reorder the terms: -1.25 + k = -2.136000936 Solving -1.25 + k = -2.136000936 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + k = -2.136000936 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + k = -2.136000936 + 1.25 k = -2.136000936 + 1.25 Combine like terms: -2.136000936 + 1.25 = -0.886000936 k = -0.886000936 Simplifying k = -0.886000936Solution
The solution to the problem is based on the solutions from the subproblems. k = {3.386000936, -0.886000936}Solution
k = {3.386000936, -0.886000936}
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