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Simplifying k2 = -17 + -9k Solving k2 = -17 + -9k Solving for variable 'k'. Reorder the terms: 17 + 9k + k2 = -17 + -9k + 17 + 9k Reorder the terms: 17 + 9k + k2 = -17 + 17 + -9k + 9k Combine like terms: -17 + 17 = 0 17 + 9k + k2 = 0 + -9k + 9k 17 + 9k + k2 = -9k + 9k Combine like terms: -9k + 9k = 0 17 + 9k + k2 = 0 Begin completing the square. Move the constant term to the right: Add '-17' to each side of the equation. 17 + 9k + -17 + k2 = 0 + -17 Reorder the terms: 17 + -17 + 9k + k2 = 0 + -17 Combine like terms: 17 + -17 = 0 0 + 9k + k2 = 0 + -17 9k + k2 = 0 + -17 Combine like terms: 0 + -17 = -17 9k + k2 = -17 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 = -17 + 20.25 Reorder the terms: 20.25 + 9k + k2 = -17 + 20.25 Combine like terms: -17 + 20.25 = 3.25 20.25 + 9k + k2 = 3.25 Factor a perfect square on the left side: (k + 4.5)(k + 4.5) = 3.25 Calculate the square root of the right side: 1.802775638 Break this problem into two subproblems by setting (k + 4.5) equal to 1.802775638 and -1.802775638.Subproblem 1
k + 4.5 = 1.802775638 Simplifying k + 4.5 = 1.802775638 Reorder the terms: 4.5 + k = 1.802775638 Solving 4.5 + k = 1.802775638 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 = 1.802775638 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + k = 1.802775638 + -4.5 k = 1.802775638 + -4.5 Combine like terms: 1.802775638 + -4.5 = -2.697224362 k = -2.697224362 Simplifying k = -2.697224362Subproblem 2
k + 4.5 = -1.802775638 Simplifying k + 4.5 = -1.802775638 Reorder the terms: 4.5 + k = -1.802775638 Solving 4.5 + k = -1.802775638 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 = -1.802775638 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + k = -1.802775638 + -4.5 k = -1.802775638 + -4.5 Combine like terms: -1.802775638 + -4.5 = -6.302775638 k = -6.302775638 Simplifying k = -6.302775638Solution
The solution to the problem is based on the solutions from the subproblems. k = {-2.697224362, -6.302775638}
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