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Simplifying k2 + 4k + -28 = 0 Reorder the terms: -28 + 4k + k2 = 0 Solving -28 + 4k + k2 = 0 Solving for variable 'k'. Begin completing the square. Move the constant term to the right: Add '28' to each side of the equation. -28 + 4k + 28 + k2 = 0 + 28 Reorder the terms: -28 + 28 + 4k + k2 = 0 + 28 Combine like terms: -28 + 28 = 0 0 + 4k + k2 = 0 + 28 4k + k2 = 0 + 28 Combine like terms: 0 + 28 = 28 4k + k2 = 28 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 = 28 + 4 Reorder the terms: 4 + 4k + k2 = 28 + 4 Combine like terms: 28 + 4 = 32 4 + 4k + k2 = 32 Factor a perfect square on the left side: (k + 2)(k + 2) = 32 Calculate the square root of the right side: 5.656854249 Break this problem into two subproblems by setting (k + 2) equal to 5.656854249 and -5.656854249.Subproblem 1
k + 2 = 5.656854249 Simplifying k + 2 = 5.656854249 Reorder the terms: 2 + k = 5.656854249 Solving 2 + k = 5.656854249 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 = 5.656854249 + -2 Combine like terms: 2 + -2 = 0 0 + k = 5.656854249 + -2 k = 5.656854249 + -2 Combine like terms: 5.656854249 + -2 = 3.656854249 k = 3.656854249 Simplifying k = 3.656854249Subproblem 2
k + 2 = -5.656854249 Simplifying k + 2 = -5.656854249 Reorder the terms: 2 + k = -5.656854249 Solving 2 + k = -5.656854249 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 = -5.656854249 + -2 Combine like terms: 2 + -2 = 0 0 + k = -5.656854249 + -2 k = -5.656854249 + -2 Combine like terms: -5.656854249 + -2 = -7.656854249 k = -7.656854249 Simplifying k = -7.656854249Solution
The solution to the problem is based on the solutions from the subproblems. k = {3.656854249, -7.656854249}
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