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Simplifying k2 + 8k + 16 = 28 Reorder the terms: 16 + 8k + k2 = 28 Solving 16 + 8k + k2 = 28 Solving for variable 'k'. Reorder the terms: 16 + -28 + 8k + k2 = 28 + -28 Combine like terms: 16 + -28 = -12 -12 + 8k + k2 = 28 + -28 Combine like terms: 28 + -28 = 0 -12 + 8k + k2 = 0 Begin completing the square. Move the constant term to the right: Add '12' to each side of the equation. -12 + 8k + 12 + k2 = 0 + 12 Reorder the terms: -12 + 12 + 8k + k2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + 8k + k2 = 0 + 12 8k + k2 = 0 + 12 Combine like terms: 0 + 12 = 12 8k + k2 = 12 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 = 12 + 16 Reorder the terms: 16 + 8k + k2 = 12 + 16 Combine like terms: 12 + 16 = 28 16 + 8k + k2 = 28 Factor a perfect square on the left side: (k + 4)(k + 4) = 28 Calculate the square root of the right side: 5.291502622 Break this problem into two subproblems by setting (k + 4) equal to 5.291502622 and -5.291502622.Subproblem 1
k + 4 = 5.291502622 Simplifying k + 4 = 5.291502622 Reorder the terms: 4 + k = 5.291502622 Solving 4 + k = 5.291502622 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 = 5.291502622 + -4 Combine like terms: 4 + -4 = 0 0 + k = 5.291502622 + -4 k = 5.291502622 + -4 Combine like terms: 5.291502622 + -4 = 1.291502622 k = 1.291502622 Simplifying k = 1.291502622Subproblem 2
k + 4 = -5.291502622 Simplifying k + 4 = -5.291502622 Reorder the terms: 4 + k = -5.291502622 Solving 4 + k = -5.291502622 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 = -5.291502622 + -4 Combine like terms: 4 + -4 = 0 0 + k = -5.291502622 + -4 k = -5.291502622 + -4 Combine like terms: -5.291502622 + -4 = -9.291502622 k = -9.291502622 Simplifying k = -9.291502622Solution
The solution to the problem is based on the solutions from the subproblems. k = {1.291502622, -9.291502622}
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