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Simplifying (k * k) + -9k = -2 Multiply k * k (k2) + -9k = -2 k2 + -9k = -2 Reorder the terms: -9k + k2 = -2 Solving -9k + k2 = -2 Solving for variable 'k'. Reorder the terms: 2 + -9k + k2 = -2 + 2 Combine like terms: -2 + 2 = 0 2 + -9k + k2 = 0 Begin completing the square. Move the constant term to the right: Add '-2' to each side of the equation. 2 + -9k + -2 + k2 = 0 + -2 Reorder the terms: 2 + -2 + -9k + k2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -9k + k2 = 0 + -2 -9k + k2 = 0 + -2 Combine like terms: 0 + -2 = -2 -9k + k2 = -2 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 = -2 + 20.25 Reorder the terms: 20.25 + -9k + k2 = -2 + 20.25 Combine like terms: -2 + 20.25 = 18.25 20.25 + -9k + k2 = 18.25 Factor a perfect square on the left side: (k + -4.5)(k + -4.5) = 18.25 Calculate the square root of the right side: 4.272001873 Break this problem into two subproblems by setting (k + -4.5) equal to 4.272001873 and -4.272001873.Subproblem 1
k + -4.5 = 4.272001873 Simplifying k + -4.5 = 4.272001873 Reorder the terms: -4.5 + k = 4.272001873 Solving -4.5 + k = 4.272001873 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 = 4.272001873 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + k = 4.272001873 + 4.5 k = 4.272001873 + 4.5 Combine like terms: 4.272001873 + 4.5 = 8.772001873 k = 8.772001873 Simplifying k = 8.772001873Subproblem 2
k + -4.5 = -4.272001873 Simplifying k + -4.5 = -4.272001873 Reorder the terms: -4.5 + k = -4.272001873 Solving -4.5 + k = -4.272001873 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 = -4.272001873 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + k = -4.272001873 + 4.5 k = -4.272001873 + 4.5 Combine like terms: -4.272001873 + 4.5 = 0.227998127 k = 0.227998127 Simplifying k = 0.227998127Solution
The solution to the problem is based on the solutions from the subproblems. k = {8.772001873, 0.227998127}
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