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Simplifying k2 + 8k + 30 = 72 Reorder the terms: 30 + 8k + k2 = 72 Solving 30 + 8k + k2 = 72 Solving for variable 'k'. Reorder the terms: 30 + -72 + 8k + k2 = 72 + -72 Combine like terms: 30 + -72 = -42 -42 + 8k + k2 = 72 + -72 Combine like terms: 72 + -72 = 0 -42 + 8k + k2 = 0 Begin completing the square. Move the constant term to the right: Add '42' to each side of the equation. -42 + 8k + 42 + k2 = 0 + 42 Reorder the terms: -42 + 42 + 8k + k2 = 0 + 42 Combine like terms: -42 + 42 = 0 0 + 8k + k2 = 0 + 42 8k + k2 = 0 + 42 Combine like terms: 0 + 42 = 42 8k + k2 = 42 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 = 42 + 16 Reorder the terms: 16 + 8k + k2 = 42 + 16 Combine like terms: 42 + 16 = 58 16 + 8k + k2 = 58 Factor a perfect square on the left side: (k + 4)(k + 4) = 58 Calculate the square root of the right side: 7.615773106 Break this problem into two subproblems by setting (k + 4) equal to 7.615773106 and -7.615773106.Subproblem 1
k + 4 = 7.615773106 Simplifying k + 4 = 7.615773106 Reorder the terms: 4 + k = 7.615773106 Solving 4 + k = 7.615773106 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 = 7.615773106 + -4 Combine like terms: 4 + -4 = 0 0 + k = 7.615773106 + -4 k = 7.615773106 + -4 Combine like terms: 7.615773106 + -4 = 3.615773106 k = 3.615773106 Simplifying k = 3.615773106Subproblem 2
k + 4 = -7.615773106 Simplifying k + 4 = -7.615773106 Reorder the terms: 4 + k = -7.615773106 Solving 4 + k = -7.615773106 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 = -7.615773106 + -4 Combine like terms: 4 + -4 = 0 0 + k = -7.615773106 + -4 k = -7.615773106 + -4 Combine like terms: -7.615773106 + -4 = -11.615773106 k = -11.615773106 Simplifying k = -11.615773106Solution
The solution to the problem is based on the solutions from the subproblems. k = {3.615773106, -11.615773106}
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