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Simplifying k2 + 9k + 4 = 0 Reorder the terms: 4 + 9k + k2 = 0 Solving 4 + 9k + k2 = 0 Solving for variable 'k'. Begin completing the square. Move the constant term to the right: Add '-4' to each side of the equation. 4 + 9k + -4 + k2 = 0 + -4 Reorder the terms: 4 + -4 + 9k + k2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 9k + k2 = 0 + -4 9k + k2 = 0 + -4 Combine like terms: 0 + -4 = -4 9k + k2 = -4 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 = -4 + 20.25 Reorder the terms: 20.25 + 9k + k2 = -4 + 20.25 Combine like terms: -4 + 20.25 = 16.25 20.25 + 9k + k2 = 16.25 Factor a perfect square on the left side: (k + 4.5)(k + 4.5) = 16.25 Calculate the square root of the right side: 4.031128874 Break this problem into two subproblems by setting (k + 4.5) equal to 4.031128874 and -4.031128874.Subproblem 1
k + 4.5 = 4.031128874 Simplifying k + 4.5 = 4.031128874 Reorder the terms: 4.5 + k = 4.031128874 Solving 4.5 + k = 4.031128874 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 = 4.031128874 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + k = 4.031128874 + -4.5 k = 4.031128874 + -4.5 Combine like terms: 4.031128874 + -4.5 = -0.468871126 k = -0.468871126 Simplifying k = -0.468871126Subproblem 2
k + 4.5 = -4.031128874 Simplifying k + 4.5 = -4.031128874 Reorder the terms: 4.5 + k = -4.031128874 Solving 4.5 + k = -4.031128874 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 = -4.031128874 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + k = -4.031128874 + -4.5 k = -4.031128874 + -4.5 Combine like terms: -4.031128874 + -4.5 = -8.531128874 k = -8.531128874 Simplifying k = -8.531128874Solution
The solution to the problem is based on the solutions from the subproblems. k = {-0.468871126, -8.531128874}
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