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Simplifying -4k2 + -104k = 68 Reorder the terms: -104k + -4k2 = 68 Solving -104k + -4k2 = 68 Solving for variable 'k'. Reorder the terms: -68 + -104k + -4k2 = 68 + -68 Combine like terms: 68 + -68 = 0 -68 + -104k + -4k2 = 0 Factor out the Greatest Common Factor (GCF), '-4'. -4(17 + 26k + k2) = 0 Ignore the factor -4.Subproblem 1
Set the factor '(17 + 26k + k2)' equal to zero and attempt to solve: Simplifying 17 + 26k + k2 = 0 Solving 17 + 26k + k2 = 0 Begin completing the square. Move the constant term to the right: Add '-17' to each side of the equation. 17 + 26k + -17 + k2 = 0 + -17 Reorder the terms: 17 + -17 + 26k + k2 = 0 + -17 Combine like terms: 17 + -17 = 0 0 + 26k + k2 = 0 + -17 26k + k2 = 0 + -17 Combine like terms: 0 + -17 = -17 26k + k2 = -17 The k term is 26k. Take half its coefficient (13). Square it (169) and add it to both sides. Add '169' to each side of the equation. 26k + 169 + k2 = -17 + 169 Reorder the terms: 169 + 26k + k2 = -17 + 169 Combine like terms: -17 + 169 = 152 169 + 26k + k2 = 152 Factor a perfect square on the left side: (k + 13)(k + 13) = 152 Calculate the square root of the right side: 12.328828006 Break this problem into two subproblems by setting (k + 13) equal to 12.328828006 and -12.328828006.Subproblem 1
k + 13 = 12.328828006 Simplifying k + 13 = 12.328828006 Reorder the terms: 13 + k = 12.328828006 Solving 13 + k = 12.328828006 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + k = 12.328828006 + -13 Combine like terms: 13 + -13 = 0 0 + k = 12.328828006 + -13 k = 12.328828006 + -13 Combine like terms: 12.328828006 + -13 = -0.671171994 k = -0.671171994 Simplifying k = -0.671171994Subproblem 2
k + 13 = -12.328828006 Simplifying k + 13 = -12.328828006 Reorder the terms: 13 + k = -12.328828006 Solving 13 + k = -12.328828006 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + k = -12.328828006 + -13 Combine like terms: 13 + -13 = 0 0 + k = -12.328828006 + -13 k = -12.328828006 + -13 Combine like terms: -12.328828006 + -13 = -25.328828006 k = -25.328828006 Simplifying k = -25.328828006Solution
The solution to the problem is based on the solutions from the subproblems. k = {-0.671171994, -25.328828006}Solution
k = {-0.671171994, -25.328828006}
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