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Simplifying k2 + 5k + -16 = 0 Reorder the terms: -16 + 5k + k2 = 0 Solving -16 + 5k + k2 = 0 Solving for variable 'k'. Begin completing the square. Move the constant term to the right: Add '16' to each side of the equation. -16 + 5k + 16 + k2 = 0 + 16 Reorder the terms: -16 + 16 + 5k + k2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + 5k + k2 = 0 + 16 5k + k2 = 0 + 16 Combine like terms: 0 + 16 = 16 5k + k2 = 16 The k term is 5k. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5k + 6.25 + k2 = 16 + 6.25 Reorder the terms: 6.25 + 5k + k2 = 16 + 6.25 Combine like terms: 16 + 6.25 = 22.25 6.25 + 5k + k2 = 22.25 Factor a perfect square on the left side: (k + 2.5)(k + 2.5) = 22.25 Calculate the square root of the right side: 4.716990566 Break this problem into two subproblems by setting (k + 2.5) equal to 4.716990566 and -4.716990566.Subproblem 1
k + 2.5 = 4.716990566 Simplifying k + 2.5 = 4.716990566 Reorder the terms: 2.5 + k = 4.716990566 Solving 2.5 + k = 4.716990566 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + k = 4.716990566 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + k = 4.716990566 + -2.5 k = 4.716990566 + -2.5 Combine like terms: 4.716990566 + -2.5 = 2.216990566 k = 2.216990566 Simplifying k = 2.216990566Subproblem 2
k + 2.5 = -4.716990566 Simplifying k + 2.5 = -4.716990566 Reorder the terms: 2.5 + k = -4.716990566 Solving 2.5 + k = -4.716990566 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + k = -4.716990566 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + k = -4.716990566 + -2.5 k = -4.716990566 + -2.5 Combine like terms: -4.716990566 + -2.5 = -7.216990566 k = -7.216990566 Simplifying k = -7.216990566Solution
The solution to the problem is based on the solutions from the subproblems. k = {2.216990566, -7.216990566}
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