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Simplifying k2 + 9k + 15 = 0 Reorder the terms: 15 + 9k + k2 = 0 Solving 15 + 9k + k2 = 0 Solving for variable 'k'. Begin completing the square. Move the constant term to the right: Add '-15' to each side of the equation. 15 + 9k + -15 + k2 = 0 + -15 Reorder the terms: 15 + -15 + 9k + k2 = 0 + -15 Combine like terms: 15 + -15 = 0 0 + 9k + k2 = 0 + -15 9k + k2 = 0 + -15 Combine like terms: 0 + -15 = -15 9k + k2 = -15 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 = -15 + 20.25 Reorder the terms: 20.25 + 9k + k2 = -15 + 20.25 Combine like terms: -15 + 20.25 = 5.25 20.25 + 9k + k2 = 5.25 Factor a perfect square on the left side: (k + 4.5)(k + 4.5) = 5.25 Calculate the square root of the right side: 2.291287847 Break this problem into two subproblems by setting (k + 4.5) equal to 2.291287847 and -2.291287847.Subproblem 1
k + 4.5 = 2.291287847 Simplifying k + 4.5 = 2.291287847 Reorder the terms: 4.5 + k = 2.291287847 Solving 4.5 + k = 2.291287847 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 = 2.291287847 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + k = 2.291287847 + -4.5 k = 2.291287847 + -4.5 Combine like terms: 2.291287847 + -4.5 = -2.208712153 k = -2.208712153 Simplifying k = -2.208712153Subproblem 2
k + 4.5 = -2.291287847 Simplifying k + 4.5 = -2.291287847 Reorder the terms: 4.5 + k = -2.291287847 Solving 4.5 + k = -2.291287847 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 = -2.291287847 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + k = -2.291287847 + -4.5 k = -2.291287847 + -4.5 Combine like terms: -2.291287847 + -4.5 = -6.791287847 k = -6.791287847 Simplifying k = -6.791287847Solution
The solution to the problem is based on the solutions from the subproblems. k = {-2.208712153, -6.791287847}
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