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Simplifying (k + 2)(k + 2) = 28 Reorder the terms: (2 + k)(k + 2) = 28 Reorder the terms: (2 + k)(2 + k) = 28 Multiply (2 + k) * (2 + k) (2(2 + k) + k(2 + k)) = 28 ((2 * 2 + k * 2) + k(2 + k)) = 28 ((4 + 2k) + k(2 + k)) = 28 (4 + 2k + (2 * k + k * k)) = 28 (4 + 2k + (2k + k2)) = 28 Combine like terms: 2k + 2k = 4k (4 + 4k + k2) = 28 Solving 4 + 4k + k2 = 28 Solving for variable 'k'. Reorder the terms: 4 + -28 + 4k + k2 = 28 + -28 Combine like terms: 4 + -28 = -24 -24 + 4k + k2 = 28 + -28 Combine like terms: 28 + -28 = 0 -24 + 4k + k2 = 0 Begin completing the square. Move the constant term to the right: Add '24' to each side of the equation. -24 + 4k + 24 + k2 = 0 + 24 Reorder the terms: -24 + 24 + 4k + k2 = 0 + 24 Combine like terms: -24 + 24 = 0 0 + 4k + k2 = 0 + 24 4k + k2 = 0 + 24 Combine like terms: 0 + 24 = 24 4k + k2 = 24 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 = 24 + 4 Reorder the terms: 4 + 4k + k2 = 24 + 4 Combine like terms: 24 + 4 = 28 4 + 4k + k2 = 28 Factor a perfect square on the left side: (k + 2)(k + 2) = 28 Calculate the square root of the right side: 5.291502622 Break this problem into two subproblems by setting (k + 2) equal to 5.291502622 and -5.291502622.Subproblem 1
k + 2 = 5.291502622 Simplifying k + 2 = 5.291502622 Reorder the terms: 2 + k = 5.291502622 Solving 2 + k = 5.291502622 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 = 5.291502622 + -2 Combine like terms: 2 + -2 = 0 0 + k = 5.291502622 + -2 k = 5.291502622 + -2 Combine like terms: 5.291502622 + -2 = 3.291502622 k = 3.291502622 Simplifying k = 3.291502622Subproblem 2
k + 2 = -5.291502622 Simplifying k + 2 = -5.291502622 Reorder the terms: 2 + k = -5.291502622 Solving 2 + k = -5.291502622 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 = -5.291502622 + -2 Combine like terms: 2 + -2 = 0 0 + k = -5.291502622 + -2 k = -5.291502622 + -2 Combine like terms: -5.291502622 + -2 = -7.291502622 k = -7.291502622 Simplifying k = -7.291502622Solution
The solution to the problem is based on the solutions from the subproblems. k = {3.291502622, -7.291502622}
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