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Simplifying k2 + -4k + -25 = 0 Reorder the terms: -25 + -4k + k2 = 0 Solving -25 + -4k + k2 = 0 Solving for variable 'k'. Begin completing the square. Move the constant term to the right: Add '25' to each side of the equation. -25 + -4k + 25 + k2 = 0 + 25 Reorder the terms: -25 + 25 + -4k + k2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + -4k + k2 = 0 + 25 -4k + k2 = 0 + 25 Combine like terms: 0 + 25 = 25 -4k + k2 = 25 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 = 25 + 4 Reorder the terms: 4 + -4k + k2 = 25 + 4 Combine like terms: 25 + 4 = 29 4 + -4k + k2 = 29 Factor a perfect square on the left side: (k + -2)(k + -2) = 29 Calculate the square root of the right side: 5.385164807 Break this problem into two subproblems by setting (k + -2) equal to 5.385164807 and -5.385164807.Subproblem 1
k + -2 = 5.385164807 Simplifying k + -2 = 5.385164807 Reorder the terms: -2 + k = 5.385164807 Solving -2 + k = 5.385164807 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 = 5.385164807 + 2 Combine like terms: -2 + 2 = 0 0 + k = 5.385164807 + 2 k = 5.385164807 + 2 Combine like terms: 5.385164807 + 2 = 7.385164807 k = 7.385164807 Simplifying k = 7.385164807Subproblem 2
k + -2 = -5.385164807 Simplifying k + -2 = -5.385164807 Reorder the terms: -2 + k = -5.385164807 Solving -2 + k = -5.385164807 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 = -5.385164807 + 2 Combine like terms: -2 + 2 = 0 0 + k = -5.385164807 + 2 k = -5.385164807 + 2 Combine like terms: -5.385164807 + 2 = -3.385164807 k = -3.385164807 Simplifying k = -3.385164807Solution
The solution to the problem is based on the solutions from the subproblems. k = {7.385164807, -3.385164807}
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