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Simplifying k2 + 9k + -28 = 0 Reorder the terms: -28 + 9k + k2 = 0 Solving -28 + 9k + 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 + 9k + 28 + k2 = 0 + 28 Reorder the terms: -28 + 28 + 9k + k2 = 0 + 28 Combine like terms: -28 + 28 = 0 0 + 9k + k2 = 0 + 28 9k + k2 = 0 + 28 Combine like terms: 0 + 28 = 28 9k + k2 = 28 The k term is 9k. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9k + 20.25 + k2 = 28 + 20.25 Reorder the terms: 20.25 + 9k + k2 = 28 + 20.25 Combine like terms: 28 + 20.25 = 48.25 20.25 + 9k + k2 = 48.25 Factor a perfect square on the left side: (k + 4.5)(k + 4.5) = 48.25 Calculate the square root of the right side: 6.946221995 Break this problem into two subproblems by setting (k + 4.5) equal to 6.946221995 and -6.946221995.Subproblem 1
k + 4.5 = 6.946221995 Simplifying k + 4.5 = 6.946221995 Reorder the terms: 4.5 + k = 6.946221995 Solving 4.5 + k = 6.946221995 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + k = 6.946221995 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + k = 6.946221995 + -4.5 k = 6.946221995 + -4.5 Combine like terms: 6.946221995 + -4.5 = 2.446221995 k = 2.446221995 Simplifying k = 2.446221995Subproblem 2
k + 4.5 = -6.946221995 Simplifying k + 4.5 = -6.946221995 Reorder the terms: 4.5 + k = -6.946221995 Solving 4.5 + k = -6.946221995 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + k = -6.946221995 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + k = -6.946221995 + -4.5 k = -6.946221995 + -4.5 Combine like terms: -6.946221995 + -4.5 = -11.446221995 k = -11.446221995 Simplifying k = -11.446221995Solution
The solution to the problem is based on the solutions from the subproblems. k = {2.446221995, -11.446221995}
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