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Simplifying 5k(k + -2) + -8k = 34 Reorder the terms: 5k(-2 + k) + -8k = 34 (-2 * 5k + k * 5k) + -8k = 34 (-10k + 5k2) + -8k = 34 Reorder the terms: -10k + -8k + 5k2 = 34 Combine like terms: -10k + -8k = -18k -18k + 5k2 = 34 Solving -18k + 5k2 = 34 Solving for variable 'k'. Reorder the terms: -34 + -18k + 5k2 = 34 + -34 Combine like terms: 34 + -34 = 0 -34 + -18k + 5k2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -6.8 + -3.6k + k2 = 0 Move the constant term to the right: Add '6.8' to each side of the equation. -6.8 + -3.6k + 6.8 + k2 = 0 + 6.8 Reorder the terms: -6.8 + 6.8 + -3.6k + k2 = 0 + 6.8 Combine like terms: -6.8 + 6.8 = 0.0 0.0 + -3.6k + k2 = 0 + 6.8 -3.6k + k2 = 0 + 6.8 Combine like terms: 0 + 6.8 = 6.8 -3.6k + k2 = 6.8 The k term is -3.6k. Take half its coefficient (-1.8). Square it (3.24) and add it to both sides. Add '3.24' to each side of the equation. -3.6k + 3.24 + k2 = 6.8 + 3.24 Reorder the terms: 3.24 + -3.6k + k2 = 6.8 + 3.24 Combine like terms: 6.8 + 3.24 = 10.04 3.24 + -3.6k + k2 = 10.04 Factor a perfect square on the left side: (k + -1.8)(k + -1.8) = 10.04 Calculate the square root of the right side: 3.168595904 Break this problem into two subproblems by setting (k + -1.8) equal to 3.168595904 and -3.168595904.Subproblem 1
k + -1.8 = 3.168595904 Simplifying k + -1.8 = 3.168595904 Reorder the terms: -1.8 + k = 3.168595904 Solving -1.8 + k = 3.168595904 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '1.8' to each side of the equation. -1.8 + 1.8 + k = 3.168595904 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + k = 3.168595904 + 1.8 k = 3.168595904 + 1.8 Combine like terms: 3.168595904 + 1.8 = 4.968595904 k = 4.968595904 Simplifying k = 4.968595904Subproblem 2
k + -1.8 = -3.168595904 Simplifying k + -1.8 = -3.168595904 Reorder the terms: -1.8 + k = -3.168595904 Solving -1.8 + k = -3.168595904 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '1.8' to each side of the equation. -1.8 + 1.8 + k = -3.168595904 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + k = -3.168595904 + 1.8 k = -3.168595904 + 1.8 Combine like terms: -3.168595904 + 1.8 = -1.368595904 k = -1.368595904 Simplifying k = -1.368595904Solution
The solution to the problem is based on the solutions from the subproblems. k = {4.968595904, -1.368595904}
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