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Simplifying k2 + 4k = 9 Reorder the terms: 4k + k2 = 9 Solving 4k + k2 = 9 Solving for variable 'k'. Reorder the terms: -9 + 4k + k2 = 9 + -9 Combine like terms: 9 + -9 = 0 -9 + 4k + k2 = 0 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 = 1.605551275 k = 1.605551275 Simplifying k = 1.605551275Subproblem 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 = -5.605551275 k = -5.605551275 Simplifying k = -5.605551275Solution
The solution to the problem is based on the solutions from the subproblems. k = {1.605551275, -5.605551275}
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