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Simplifying 38k + 7k = 8k(k + 4) Combine like terms: 38k + 7k = 45k 45k = 8k(k + 4) Reorder the terms: 45k = 8k(4 + k) 45k = (4 * 8k + k * 8k) 45k = (32k + 8k2) Solving 45k = 32k + 8k2 Solving for variable 'k'. Combine like terms: 45k + -32k = 13k 13k + -8k2 = 32k + 8k2 + -32k + -8k2 Reorder the terms: 13k + -8k2 = 32k + -32k + 8k2 + -8k2 Combine like terms: 32k + -32k = 0 13k + -8k2 = 0 + 8k2 + -8k2 13k + -8k2 = 8k2 + -8k2 Combine like terms: 8k2 + -8k2 = 0 13k + -8k2 = 0 Factor out the Greatest Common Factor (GCF), 'k'. k(13 + -8k) = 0Subproblem 1
Set the factor 'k' equal to zero and attempt to solve: Simplifying k = 0 Solving k = 0 Move all terms containing k to the left, all other terms to the right. Simplifying k = 0Subproblem 2
Set the factor '(13 + -8k)' equal to zero and attempt to solve: Simplifying 13 + -8k = 0 Solving 13 + -8k = 0 Move all terms containing k to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + -8k = 0 + -13 Combine like terms: 13 + -13 = 0 0 + -8k = 0 + -13 -8k = 0 + -13 Combine like terms: 0 + -13 = -13 -8k = -13 Divide each side by '-8'. k = 1.625 Simplifying k = 1.625Solution
k = {0, 1.625}
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