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Simplifying k2 + -4k + -9 = 0 Reorder the terms: -9 + -4k + k2 = 0 Solving -9 + -4k + k2 = 0 Solving for variable 'k'. Begin completing the square. Move the constant term to the right: Add '9' to each side of the equation. -9 + -4k + 9 + k2 = 0 + 9 Reorder the terms: -9 + 9 + -4k + k2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -4k + k2 = 0 + 9 -4k + k2 = 0 + 9 Combine like terms: 0 + 9 = 9 -4k + k2 = 9 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 = 9 + 4 Reorder the terms: 4 + -4k + k2 = 9 + 4 Combine like terms: 9 + 4 = 13 4 + -4k + k2 = 13 Factor a perfect square on the left side: (k + -2)(k + -2) = 13 Calculate the square root of the right side: 3.605551275 Break this problem into two subproblems by setting (k + -2) equal to 3.605551275 and -3.605551275.Subproblem 1
k + -2 = 3.605551275 Simplifying k + -2 = 3.605551275 Reorder the terms: -2 + k = 3.605551275 Solving -2 + k = 3.605551275 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 = 3.605551275 + 2 Combine like terms: -2 + 2 = 0 0 + k = 3.605551275 + 2 k = 3.605551275 + 2 Combine like terms: 3.605551275 + 2 = 5.605551275 k = 5.605551275 Simplifying k = 5.605551275Subproblem 2
k + -2 = -3.605551275 Simplifying k + -2 = -3.605551275 Reorder the terms: -2 + k = -3.605551275 Solving -2 + k = -3.605551275 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 = -3.605551275 + 2 Combine like terms: -2 + 2 = 0 0 + k = -3.605551275 + 2 k = -3.605551275 + 2 Combine like terms: -3.605551275 + 2 = -1.605551275 k = -1.605551275 Simplifying k = -1.605551275Solution
The solution to the problem is based on the solutions from the subproblems. k = {5.605551275, -1.605551275}
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