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Simplifying -2k2 + -16k = -32 Reorder the terms: -16k + -2k2 = -32 Solving -16k + -2k2 = -32 Solving for variable 'k'. Reorder the terms: 32 + -16k + -2k2 = -32 + 32 Combine like terms: -32 + 32 = 0 32 + -16k + -2k2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(16 + -8k + -1k2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(16 + -8k + -1k2)' equal to zero and attempt to solve: Simplifying 16 + -8k + -1k2 = 0 Solving 16 + -8k + -1k2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -16 + 8k + k2 = 0 Move the constant term to the right: Add '16' to each side of the equation. -16 + 8k + 16 + k2 = 0 + 16 Reorder the terms: -16 + 16 + 8k + k2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + 8k + k2 = 0 + 16 8k + k2 = 0 + 16 Combine like terms: 0 + 16 = 16 8k + k2 = 16 The k term is 8k. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8k + 16 + k2 = 16 + 16 Reorder the terms: 16 + 8k + k2 = 16 + 16 Combine like terms: 16 + 16 = 32 16 + 8k + k2 = 32 Factor a perfect square on the left side: (k + 4)(k + 4) = 32 Calculate the square root of the right side: 5.656854249 Break this problem into two subproblems by setting (k + 4) equal to 5.656854249 and -5.656854249.Subproblem 1
k + 4 = 5.656854249 Simplifying k + 4 = 5.656854249 Reorder the terms: 4 + k = 5.656854249 Solving 4 + k = 5.656854249 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + k = 5.656854249 + -4 Combine like terms: 4 + -4 = 0 0 + k = 5.656854249 + -4 k = 5.656854249 + -4 Combine like terms: 5.656854249 + -4 = 1.656854249 k = 1.656854249 Simplifying k = 1.656854249Subproblem 2
k + 4 = -5.656854249 Simplifying k + 4 = -5.656854249 Reorder the terms: 4 + k = -5.656854249 Solving 4 + k = -5.656854249 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + k = -5.656854249 + -4 Combine like terms: 4 + -4 = 0 0 + k = -5.656854249 + -4 k = -5.656854249 + -4 Combine like terms: -5.656854249 + -4 = -9.656854249 k = -9.656854249 Simplifying k = -9.656854249Solution
The solution to the problem is based on the solutions from the subproblems. k = {1.656854249, -9.656854249}Solution
k = {1.656854249, -9.656854249}
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