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Simplifying k2 + -32k + 8 = 0 Reorder the terms: 8 + -32k + k2 = 0 Solving 8 + -32k + k2 = 0 Solving for variable 'k'. Begin completing the square. Move the constant term to the right: Add '-8' to each side of the equation. 8 + -32k + -8 + k2 = 0 + -8 Reorder the terms: 8 + -8 + -32k + k2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -32k + k2 = 0 + -8 -32k + k2 = 0 + -8 Combine like terms: 0 + -8 = -8 -32k + k2 = -8 The k term is -32k. Take half its coefficient (-16). Square it (256) and add it to both sides. Add '256' to each side of the equation. -32k + 256 + k2 = -8 + 256 Reorder the terms: 256 + -32k + k2 = -8 + 256 Combine like terms: -8 + 256 = 248 256 + -32k + k2 = 248 Factor a perfect square on the left side: (k + -16)(k + -16) = 248 Calculate the square root of the right side: 15.748015748 Break this problem into two subproblems by setting (k + -16) equal to 15.748015748 and -15.748015748.Subproblem 1
k + -16 = 15.748015748 Simplifying k + -16 = 15.748015748 Reorder the terms: -16 + k = 15.748015748 Solving -16 + k = 15.748015748 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '16' to each side of the equation. -16 + 16 + k = 15.748015748 + 16 Combine like terms: -16 + 16 = 0 0 + k = 15.748015748 + 16 k = 15.748015748 + 16 Combine like terms: 15.748015748 + 16 = 31.748015748 k = 31.748015748 Simplifying k = 31.748015748Subproblem 2
k + -16 = -15.748015748 Simplifying k + -16 = -15.748015748 Reorder the terms: -16 + k = -15.748015748 Solving -16 + k = -15.748015748 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '16' to each side of the equation. -16 + 16 + k = -15.748015748 + 16 Combine like terms: -16 + 16 = 0 0 + k = -15.748015748 + 16 k = -15.748015748 + 16 Combine like terms: -15.748015748 + 16 = 0.251984252 k = 0.251984252 Simplifying k = 0.251984252Solution
The solution to the problem is based on the solutions from the subproblems. k = {31.748015748, 0.251984252}
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