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Simplifying 2k2 = 9 + 34k Solving 2k2 = 9 + 34k Solving for variable 'k'. Reorder the terms: -9 + -34k + 2k2 = 9 + 34k + -9 + -34k Reorder the terms: -9 + -34k + 2k2 = 9 + -9 + 34k + -34k Combine like terms: 9 + -9 = 0 -9 + -34k + 2k2 = 0 + 34k + -34k -9 + -34k + 2k2 = 34k + -34k Combine like terms: 34k + -34k = 0 -9 + -34k + 2k2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -4.5 + -17k + k2 = 0 Move the constant term to the right: Add '4.5' to each side of the equation. -4.5 + -17k + 4.5 + k2 = 0 + 4.5 Reorder the terms: -4.5 + 4.5 + -17k + k2 = 0 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + -17k + k2 = 0 + 4.5 -17k + k2 = 0 + 4.5 Combine like terms: 0 + 4.5 = 4.5 -17k + k2 = 4.5 The k term is -17k. Take half its coefficient (-8.5). Square it (72.25) and add it to both sides. Add '72.25' to each side of the equation. -17k + 72.25 + k2 = 4.5 + 72.25 Reorder the terms: 72.25 + -17k + k2 = 4.5 + 72.25 Combine like terms: 4.5 + 72.25 = 76.75 72.25 + -17k + k2 = 76.75 Factor a perfect square on the left side: (k + -8.5)(k + -8.5) = 76.75 Calculate the square root of the right side: 8.760707734 Break this problem into two subproblems by setting (k + -8.5) equal to 8.760707734 and -8.760707734.Subproblem 1
k + -8.5 = 8.760707734 Simplifying k + -8.5 = 8.760707734 Reorder the terms: -8.5 + k = 8.760707734 Solving -8.5 + k = 8.760707734 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + k = 8.760707734 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + k = 8.760707734 + 8.5 k = 8.760707734 + 8.5 Combine like terms: 8.760707734 + 8.5 = 17.260707734 k = 17.260707734 Simplifying k = 17.260707734Subproblem 2
k + -8.5 = -8.760707734 Simplifying k + -8.5 = -8.760707734 Reorder the terms: -8.5 + k = -8.760707734 Solving -8.5 + k = -8.760707734 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + k = -8.760707734 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + k = -8.760707734 + 8.5 k = -8.760707734 + 8.5 Combine like terms: -8.760707734 + 8.5 = -0.260707734 k = -0.260707734 Simplifying k = -0.260707734Solution
The solution to the problem is based on the solutions from the subproblems. k = {17.260707734, -0.260707734}
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