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Simplifying k2 + 4k + -53 = 0 Reorder the terms: -53 + 4k + k2 = 0 Solving -53 + 4k + k2 = 0 Solving for variable 'k'. Begin completing the square. Move the constant term to the right: Add '53' to each side of the equation. -53 + 4k + 53 + k2 = 0 + 53 Reorder the terms: -53 + 53 + 4k + k2 = 0 + 53 Combine like terms: -53 + 53 = 0 0 + 4k + k2 = 0 + 53 4k + k2 = 0 + 53 Combine like terms: 0 + 53 = 53 4k + k2 = 53 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 = 53 + 4 Reorder the terms: 4 + 4k + k2 = 53 + 4 Combine like terms: 53 + 4 = 57 4 + 4k + k2 = 57 Factor a perfect square on the left side: (k + 2)(k + 2) = 57 Calculate the square root of the right side: 7.549834435 Break this problem into two subproblems by setting (k + 2) equal to 7.549834435 and -7.549834435.Subproblem 1
k + 2 = 7.549834435 Simplifying k + 2 = 7.549834435 Reorder the terms: 2 + k = 7.549834435 Solving 2 + k = 7.549834435 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 = 7.549834435 + -2 Combine like terms: 2 + -2 = 0 0 + k = 7.549834435 + -2 k = 7.549834435 + -2 Combine like terms: 7.549834435 + -2 = 5.549834435 k = 5.549834435 Simplifying k = 5.549834435Subproblem 2
k + 2 = -7.549834435 Simplifying k + 2 = -7.549834435 Reorder the terms: 2 + k = -7.549834435 Solving 2 + k = -7.549834435 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 = -7.549834435 + -2 Combine like terms: 2 + -2 = 0 0 + k = -7.549834435 + -2 k = -7.549834435 + -2 Combine like terms: -7.549834435 + -2 = -9.549834435 k = -9.549834435 Simplifying k = -9.549834435Solution
The solution to the problem is based on the solutions from the subproblems. k = {5.549834435, -9.549834435}
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