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Simplifying 16 = 7k + k2 Solving 16 = 7k + k2 Solving for variable 'k'. Reorder the terms: 16 + -7k + -1k2 = 7k + -7k + k2 + -1k2 Combine like terms: 7k + -7k = 0 16 + -7k + -1k2 = 0 + k2 + -1k2 16 + -7k + -1k2 = k2 + -1k2 Combine like terms: k2 + -1k2 = 0 16 + -7k + -1k2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -16 + 7k + k2 = 0 Move the constant term to the right: Add '16' to each side of the equation. -16 + 7k + 16 + k2 = 0 + 16 Reorder the terms: -16 + 16 + 7k + k2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + 7k + k2 = 0 + 16 7k + k2 = 0 + 16 Combine like terms: 0 + 16 = 16 7k + k2 = 16 The k term is 7k. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7k + 12.25 + k2 = 16 + 12.25 Reorder the terms: 12.25 + 7k + k2 = 16 + 12.25 Combine like terms: 16 + 12.25 = 28.25 12.25 + 7k + k2 = 28.25 Factor a perfect square on the left side: (k + 3.5)(k + 3.5) = 28.25 Calculate the square root of the right side: 5.315072906 Break this problem into two subproblems by setting (k + 3.5) equal to 5.315072906 and -5.315072906.Subproblem 1
k + 3.5 = 5.315072906 Simplifying k + 3.5 = 5.315072906 Reorder the terms: 3.5 + k = 5.315072906 Solving 3.5 + k = 5.315072906 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + k = 5.315072906 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + k = 5.315072906 + -3.5 k = 5.315072906 + -3.5 Combine like terms: 5.315072906 + -3.5 = 1.815072906 k = 1.815072906 Simplifying k = 1.815072906Subproblem 2
k + 3.5 = -5.315072906 Simplifying k + 3.5 = -5.315072906 Reorder the terms: 3.5 + k = -5.315072906 Solving 3.5 + k = -5.315072906 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + k = -5.315072906 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + k = -5.315072906 + -3.5 k = -5.315072906 + -3.5 Combine like terms: -5.315072906 + -3.5 = -8.815072906 k = -8.815072906 Simplifying k = -8.815072906Solution
The solution to the problem is based on the solutions from the subproblems. k = {1.815072906, -8.815072906}
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