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Simplifying 2k2 + 8k = 16 Reorder the terms: 8k + 2k2 = 16 Solving 8k + 2k2 = 16 Solving for variable 'k'. Reorder the terms: -16 + 8k + 2k2 = 16 + -16 Combine like terms: 16 + -16 = 0 -16 + 8k + 2k2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-8 + 4k + k2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-8 + 4k + k2)' equal to zero and attempt to solve: Simplifying -8 + 4k + k2 = 0 Solving -8 + 4k + k2 = 0 Begin completing the square. Move the constant term to the right: Add '8' to each side of the equation. -8 + 4k + 8 + k2 = 0 + 8 Reorder the terms: -8 + 8 + 4k + k2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + 4k + k2 = 0 + 8 4k + k2 = 0 + 8 Combine like terms: 0 + 8 = 8 4k + k2 = 8 The k term is 4k. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4k + 4 + k2 = 8 + 4 Reorder the terms: 4 + 4k + k2 = 8 + 4 Combine like terms: 8 + 4 = 12 4 + 4k + k2 = 12 Factor a perfect square on the left side: (k + 2)(k + 2) = 12 Calculate the square root of the right side: 3.464101615 Break this problem into two subproblems by setting (k + 2) equal to 3.464101615 and -3.464101615.Subproblem 1
k + 2 = 3.464101615 Simplifying k + 2 = 3.464101615 Reorder the terms: 2 + k = 3.464101615 Solving 2 + k = 3.464101615 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + k = 3.464101615 + -2 Combine like terms: 2 + -2 = 0 0 + k = 3.464101615 + -2 k = 3.464101615 + -2 Combine like terms: 3.464101615 + -2 = 1.464101615 k = 1.464101615 Simplifying k = 1.464101615Subproblem 2
k + 2 = -3.464101615 Simplifying k + 2 = -3.464101615 Reorder the terms: 2 + k = -3.464101615 Solving 2 + k = -3.464101615 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + k = -3.464101615 + -2 Combine like terms: 2 + -2 = 0 0 + k = -3.464101615 + -2 k = -3.464101615 + -2 Combine like terms: -3.464101615 + -2 = -5.464101615 k = -5.464101615 Simplifying k = -5.464101615Solution
The solution to the problem is based on the solutions from the subproblems. k = {1.464101615, -5.464101615}Solution
k = {1.464101615, -5.464101615}
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