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Simplifying 2k2 = 18k + -26 Reorder the terms: 2k2 = -26 + 18k Solving 2k2 = -26 + 18k Solving for variable 'k'. Reorder the terms: 26 + -18k + 2k2 = -26 + 18k + 26 + -18k Reorder the terms: 26 + -18k + 2k2 = -26 + 26 + 18k + -18k Combine like terms: -26 + 26 = 0 26 + -18k + 2k2 = 0 + 18k + -18k 26 + -18k + 2k2 = 18k + -18k Combine like terms: 18k + -18k = 0 26 + -18k + 2k2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(13 + -9k + k2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(13 + -9k + k2)' equal to zero and attempt to solve: Simplifying 13 + -9k + k2 = 0 Solving 13 + -9k + k2 = 0 Begin completing the square. Move the constant term to the right: Add '-13' to each side of the equation. 13 + -9k + -13 + k2 = 0 + -13 Reorder the terms: 13 + -13 + -9k + k2 = 0 + -13 Combine like terms: 13 + -13 = 0 0 + -9k + k2 = 0 + -13 -9k + k2 = 0 + -13 Combine like terms: 0 + -13 = -13 -9k + k2 = -13 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 = -13 + 20.25 Reorder the terms: 20.25 + -9k + k2 = -13 + 20.25 Combine like terms: -13 + 20.25 = 7.25 20.25 + -9k + k2 = 7.25 Factor a perfect square on the left side: (k + -4.5)(k + -4.5) = 7.25 Calculate the square root of the right side: 2.692582404 Break this problem into two subproblems by setting (k + -4.5) equal to 2.692582404 and -2.692582404.Subproblem 1
k + -4.5 = 2.692582404 Simplifying k + -4.5 = 2.692582404 Reorder the terms: -4.5 + k = 2.692582404 Solving -4.5 + k = 2.692582404 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 = 2.692582404 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + k = 2.692582404 + 4.5 k = 2.692582404 + 4.5 Combine like terms: 2.692582404 + 4.5 = 7.192582404 k = 7.192582404 Simplifying k = 7.192582404Subproblem 2
k + -4.5 = -2.692582404 Simplifying k + -4.5 = -2.692582404 Reorder the terms: -4.5 + k = -2.692582404 Solving -4.5 + k = -2.692582404 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 = -2.692582404 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + k = -2.692582404 + 4.5 k = -2.692582404 + 4.5 Combine like terms: -2.692582404 + 4.5 = 1.807417596 k = 1.807417596 Simplifying k = 1.807417596Solution
The solution to the problem is based on the solutions from the subproblems. k = {7.192582404, 1.807417596}Solution
k = {7.192582404, 1.807417596}
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