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Simplifying -25k + 5k2 = 25 Solving -25k + 5k2 = 25 Solving for variable 'k'. Reorder the terms: -25 + -25k + 5k2 = 25 + -25 Combine like terms: 25 + -25 = 0 -25 + -25k + 5k2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-5 + -5k + k2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-5 + -5k + k2)' equal to zero and attempt to solve: Simplifying -5 + -5k + k2 = 0 Solving -5 + -5k + k2 = 0 Begin completing the square. Move the constant term to the right: Add '5' to each side of the equation. -5 + -5k + 5 + k2 = 0 + 5 Reorder the terms: -5 + 5 + -5k + k2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -5k + k2 = 0 + 5 -5k + k2 = 0 + 5 Combine like terms: 0 + 5 = 5 -5k + k2 = 5 The k term is -5k. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5k + 6.25 + k2 = 5 + 6.25 Reorder the terms: 6.25 + -5k + k2 = 5 + 6.25 Combine like terms: 5 + 6.25 = 11.25 6.25 + -5k + k2 = 11.25 Factor a perfect square on the left side: (k + -2.5)(k + -2.5) = 11.25 Calculate the square root of the right side: 3.354101966 Break this problem into two subproblems by setting (k + -2.5) equal to 3.354101966 and -3.354101966.Subproblem 1
k + -2.5 = 3.354101966 Simplifying k + -2.5 = 3.354101966 Reorder the terms: -2.5 + k = 3.354101966 Solving -2.5 + k = 3.354101966 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + k = 3.354101966 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + k = 3.354101966 + 2.5 k = 3.354101966 + 2.5 Combine like terms: 3.354101966 + 2.5 = 5.854101966 k = 5.854101966 Simplifying k = 5.854101966Subproblem 2
k + -2.5 = -3.354101966 Simplifying k + -2.5 = -3.354101966 Reorder the terms: -2.5 + k = -3.354101966 Solving -2.5 + k = -3.354101966 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + k = -3.354101966 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + k = -3.354101966 + 2.5 k = -3.354101966 + 2.5 Combine like terms: -3.354101966 + 2.5 = -0.854101966 k = -0.854101966 Simplifying k = -0.854101966Solution
The solution to the problem is based on the solutions from the subproblems. k = {5.854101966, -0.854101966}Solution
k = {5.854101966, -0.854101966}
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