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Simplifying k2 + 32k + -28 = 0 Reorder the terms: -28 + 32k + k2 = 0 Solving -28 + 32k + 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 + 32k + 28 + k2 = 0 + 28 Reorder the terms: -28 + 28 + 32k + k2 = 0 + 28 Combine like terms: -28 + 28 = 0 0 + 32k + k2 = 0 + 28 32k + k2 = 0 + 28 Combine like terms: 0 + 28 = 28 32k + k2 = 28 The k term is 32k. Take half its coefficient (16). Square it (256) and add it to both sides. Add '256' to each side of the equation. 32k + 256 + k2 = 28 + 256 Reorder the terms: 256 + 32k + k2 = 28 + 256 Combine like terms: 28 + 256 = 284 256 + 32k + k2 = 284 Factor a perfect square on the left side: (k + 16)(k + 16) = 284 Calculate the square root of the right side: 16.852299546 Break this problem into two subproblems by setting (k + 16) equal to 16.852299546 and -16.852299546.Subproblem 1
k + 16 = 16.852299546 Simplifying k + 16 = 16.852299546 Reorder the terms: 16 + k = 16.852299546 Solving 16 + k = 16.852299546 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-16' to each side of the equation. 16 + -16 + k = 16.852299546 + -16 Combine like terms: 16 + -16 = 0 0 + k = 16.852299546 + -16 k = 16.852299546 + -16 Combine like terms: 16.852299546 + -16 = 0.852299546 k = 0.852299546 Simplifying k = 0.852299546Subproblem 2
k + 16 = -16.852299546 Simplifying k + 16 = -16.852299546 Reorder the terms: 16 + k = -16.852299546 Solving 16 + k = -16.852299546 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-16' to each side of the equation. 16 + -16 + k = -16.852299546 + -16 Combine like terms: 16 + -16 = 0 0 + k = -16.852299546 + -16 k = -16.852299546 + -16 Combine like terms: -16.852299546 + -16 = -32.852299546 k = -32.852299546 Simplifying k = -32.852299546Solution
The solution to the problem is based on the solutions from the subproblems. k = {0.852299546, -32.852299546}
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