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Simplifying k2 + 8k + 30 = 37 Reorder the terms: 30 + 8k + k2 = 37 Solving 30 + 8k + k2 = 37 Solving for variable 'k'. Reorder the terms: 30 + -37 + 8k + k2 = 37 + -37 Combine like terms: 30 + -37 = -7 -7 + 8k + k2 = 37 + -37 Combine like terms: 37 + -37 = 0 -7 + 8k + k2 = 0 Begin completing the square. Move the constant term to the right: Add '7' to each side of the equation. -7 + 8k + 7 + k2 = 0 + 7 Reorder the terms: -7 + 7 + 8k + k2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + 8k + k2 = 0 + 7 8k + k2 = 0 + 7 Combine like terms: 0 + 7 = 7 8k + k2 = 7 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 = 7 + 16 Reorder the terms: 16 + 8k + k2 = 7 + 16 Combine like terms: 7 + 16 = 23 16 + 8k + k2 = 23 Factor a perfect square on the left side: (k + 4)(k + 4) = 23 Calculate the square root of the right side: 4.795831523 Break this problem into two subproblems by setting (k + 4) equal to 4.795831523 and -4.795831523.Subproblem 1
k + 4 = 4.795831523 Simplifying k + 4 = 4.795831523 Reorder the terms: 4 + k = 4.795831523 Solving 4 + k = 4.795831523 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 = 4.795831523 + -4 Combine like terms: 4 + -4 = 0 0 + k = 4.795831523 + -4 k = 4.795831523 + -4 Combine like terms: 4.795831523 + -4 = 0.795831523 k = 0.795831523 Simplifying k = 0.795831523Subproblem 2
k + 4 = -4.795831523 Simplifying k + 4 = -4.795831523 Reorder the terms: 4 + k = -4.795831523 Solving 4 + k = -4.795831523 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 = -4.795831523 + -4 Combine like terms: 4 + -4 = 0 0 + k = -4.795831523 + -4 k = -4.795831523 + -4 Combine like terms: -4.795831523 + -4 = -8.795831523 k = -8.795831523 Simplifying k = -8.795831523Solution
The solution to the problem is based on the solutions from the subproblems. k = {0.795831523, -8.795831523}
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