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Simplifying k2 + -19k + -100 = 0 Reorder the terms: -100 + -19k + k2 = 0 Solving -100 + -19k + k2 = 0 Solving for variable 'k'. Begin completing the square. Move the constant term to the right: Add '100' to each side of the equation. -100 + -19k + 100 + k2 = 0 + 100 Reorder the terms: -100 + 100 + -19k + k2 = 0 + 100 Combine like terms: -100 + 100 = 0 0 + -19k + k2 = 0 + 100 -19k + k2 = 0 + 100 Combine like terms: 0 + 100 = 100 -19k + k2 = 100 The k term is -19k. Take half its coefficient (-9.5). Square it (90.25) and add it to both sides. Add '90.25' to each side of the equation. -19k + 90.25 + k2 = 100 + 90.25 Reorder the terms: 90.25 + -19k + k2 = 100 + 90.25 Combine like terms: 100 + 90.25 = 190.25 90.25 + -19k + k2 = 190.25 Factor a perfect square on the left side: (k + -9.5)(k + -9.5) = 190.25 Calculate the square root of the right side: 13.793114224 Break this problem into two subproblems by setting (k + -9.5) equal to 13.793114224 and -13.793114224.Subproblem 1
k + -9.5 = 13.793114224 Simplifying k + -9.5 = 13.793114224 Reorder the terms: -9.5 + k = 13.793114224 Solving -9.5 + k = 13.793114224 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + k = 13.793114224 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + k = 13.793114224 + 9.5 k = 13.793114224 + 9.5 Combine like terms: 13.793114224 + 9.5 = 23.293114224 k = 23.293114224 Simplifying k = 23.293114224Subproblem 2
k + -9.5 = -13.793114224 Simplifying k + -9.5 = -13.793114224 Reorder the terms: -9.5 + k = -13.793114224 Solving -9.5 + k = -13.793114224 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + k = -13.793114224 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + k = -13.793114224 + 9.5 k = -13.793114224 + 9.5 Combine like terms: -13.793114224 + 9.5 = -4.293114224 k = -4.293114224 Simplifying k = -4.293114224Solution
The solution to the problem is based on the solutions from the subproblems. k = {23.293114224, -4.293114224}
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