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Simplifying 8k2 + -17k + -15 = 0 Reorder the terms: -15 + -17k + 8k2 = 0 Solving -15 + -17k + 8k2 = 0 Solving for variable 'k'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -1.875 + -2.125k + k2 = 0 Move the constant term to the right: Add '1.875' to each side of the equation. -1.875 + -2.125k + 1.875 + k2 = 0 + 1.875 Reorder the terms: -1.875 + 1.875 + -2.125k + k2 = 0 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + -2.125k + k2 = 0 + 1.875 -2.125k + k2 = 0 + 1.875 Combine like terms: 0 + 1.875 = 1.875 -2.125k + k2 = 1.875 The k term is -2.125k. Take half its coefficient (-1.0625). Square it (1.12890625) and add it to both sides. Add '1.12890625' to each side of the equation. -2.125k + 1.12890625 + k2 = 1.875 + 1.12890625 Reorder the terms: 1.12890625 + -2.125k + k2 = 1.875 + 1.12890625 Combine like terms: 1.875 + 1.12890625 = 3.00390625 1.12890625 + -2.125k + k2 = 3.00390625 Factor a perfect square on the left side: (k + -1.0625)(k + -1.0625) = 3.00390625 Calculate the square root of the right side: 1.733178078 Break this problem into two subproblems by setting (k + -1.0625) equal to 1.733178078 and -1.733178078.Subproblem 1
k + -1.0625 = 1.733178078 Simplifying k + -1.0625 = 1.733178078 Reorder the terms: -1.0625 + k = 1.733178078 Solving -1.0625 + k = 1.733178078 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '1.0625' to each side of the equation. -1.0625 + 1.0625 + k = 1.733178078 + 1.0625 Combine like terms: -1.0625 + 1.0625 = 0.0000 0.0000 + k = 1.733178078 + 1.0625 k = 1.733178078 + 1.0625 Combine like terms: 1.733178078 + 1.0625 = 2.795678078 k = 2.795678078 Simplifying k = 2.795678078Subproblem 2
k + -1.0625 = -1.733178078 Simplifying k + -1.0625 = -1.733178078 Reorder the terms: -1.0625 + k = -1.733178078 Solving -1.0625 + k = -1.733178078 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '1.0625' to each side of the equation. -1.0625 + 1.0625 + k = -1.733178078 + 1.0625 Combine like terms: -1.0625 + 1.0625 = 0.0000 0.0000 + k = -1.733178078 + 1.0625 k = -1.733178078 + 1.0625 Combine like terms: -1.733178078 + 1.0625 = -0.670678078 k = -0.670678078 Simplifying k = -0.670678078Solution
The solution to the problem is based on the solutions from the subproblems. k = {2.795678078, -0.670678078}
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