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Simplifying 10k2 + -24 = -12k Reorder the terms: -24 + 10k2 = -12k Solving -24 + 10k2 = -12k Solving for variable 'k'. Reorder the terms: -24 + 12k + 10k2 = -12k + 12k Combine like terms: -12k + 12k = 0 -24 + 12k + 10k2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-12 + 6k + 5k2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-12 + 6k + 5k2)' equal to zero and attempt to solve: Simplifying -12 + 6k + 5k2 = 0 Solving -12 + 6k + 5k2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -2.4 + 1.2k + k2 = 0 Move the constant term to the right: Add '2.4' to each side of the equation. -2.4 + 1.2k + 2.4 + k2 = 0 + 2.4 Reorder the terms: -2.4 + 2.4 + 1.2k + k2 = 0 + 2.4 Combine like terms: -2.4 + 2.4 = 0.0 0.0 + 1.2k + k2 = 0 + 2.4 1.2k + k2 = 0 + 2.4 Combine like terms: 0 + 2.4 = 2.4 1.2k + k2 = 2.4 The k term is 1.2k. Take half its coefficient (0.6). Square it (0.36) and add it to both sides. Add '0.36' to each side of the equation. 1.2k + 0.36 + k2 = 2.4 + 0.36 Reorder the terms: 0.36 + 1.2k + k2 = 2.4 + 0.36 Combine like terms: 2.4 + 0.36 = 2.76 0.36 + 1.2k + k2 = 2.76 Factor a perfect square on the left side: (k + 0.6)(k + 0.6) = 2.76 Calculate the square root of the right side: 1.661324773 Break this problem into two subproblems by setting (k + 0.6) equal to 1.661324773 and -1.661324773.Subproblem 1
k + 0.6 = 1.661324773 Simplifying k + 0.6 = 1.661324773 Reorder the terms: 0.6 + k = 1.661324773 Solving 0.6 + k = 1.661324773 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-0.6' to each side of the equation. 0.6 + -0.6 + k = 1.661324773 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + k = 1.661324773 + -0.6 k = 1.661324773 + -0.6 Combine like terms: 1.661324773 + -0.6 = 1.061324773 k = 1.061324773 Simplifying k = 1.061324773Subproblem 2
k + 0.6 = -1.661324773 Simplifying k + 0.6 = -1.661324773 Reorder the terms: 0.6 + k = -1.661324773 Solving 0.6 + k = -1.661324773 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-0.6' to each side of the equation. 0.6 + -0.6 + k = -1.661324773 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + k = -1.661324773 + -0.6 k = -1.661324773 + -0.6 Combine like terms: -1.661324773 + -0.6 = -2.261324773 k = -2.261324773 Simplifying k = -2.261324773Solution
The solution to the problem is based on the solutions from the subproblems. k = {1.061324773, -2.261324773}Solution
k = {1.061324773, -2.261324773}
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