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Simplifying 2k2 + -6k + -5 = 0 Reorder the terms: -5 + -6k + 2k2 = 0 Solving -5 + -6k + 2k2 = 0 Solving for variable 'k'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -2.5 + -3k + k2 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + -3k + 2.5 + k2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + -3k + k2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + -3k + k2 = 0 + 2.5 -3k + k2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 -3k + k2 = 2.5 The k term is -3k. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3k + 2.25 + k2 = 2.5 + 2.25 Reorder the terms: 2.25 + -3k + k2 = 2.5 + 2.25 Combine like terms: 2.5 + 2.25 = 4.75 2.25 + -3k + k2 = 4.75 Factor a perfect square on the left side: (k + -1.5)(k + -1.5) = 4.75 Calculate the square root of the right side: 2.179449472 Break this problem into two subproblems by setting (k + -1.5) equal to 2.179449472 and -2.179449472.Subproblem 1
k + -1.5 = 2.179449472 Simplifying k + -1.5 = 2.179449472 Reorder the terms: -1.5 + k = 2.179449472 Solving -1.5 + k = 2.179449472 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + k = 2.179449472 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + k = 2.179449472 + 1.5 k = 2.179449472 + 1.5 Combine like terms: 2.179449472 + 1.5 = 3.679449472 k = 3.679449472 Simplifying k = 3.679449472Subproblem 2
k + -1.5 = -2.179449472 Simplifying k + -1.5 = -2.179449472 Reorder the terms: -1.5 + k = -2.179449472 Solving -1.5 + k = -2.179449472 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + k = -2.179449472 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + k = -2.179449472 + 1.5 k = -2.179449472 + 1.5 Combine like terms: -2.179449472 + 1.5 = -0.679449472 k = -0.679449472 Simplifying k = -0.679449472Solution
The solution to the problem is based on the solutions from the subproblems. k = {3.679449472, -0.679449472}
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