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Simplifying 7k2 + -57k + 102 = -1k + -3 Reorder the terms: 102 + -57k + 7k2 = -1k + -3 Reorder the terms: 102 + -57k + 7k2 = -3 + -1k Solving 102 + -57k + 7k2 = -3 + -1k Solving for variable 'k'. Reorder the terms: 102 + 3 + -57k + k + 7k2 = -3 + -1k + 3 + k Combine like terms: 102 + 3 = 105 105 + -57k + k + 7k2 = -3 + -1k + 3 + k Combine like terms: -57k + k = -56k 105 + -56k + 7k2 = -3 + -1k + 3 + k Reorder the terms: 105 + -56k + 7k2 = -3 + 3 + -1k + k Combine like terms: -3 + 3 = 0 105 + -56k + 7k2 = 0 + -1k + k 105 + -56k + 7k2 = -1k + k Combine like terms: -1k + k = 0 105 + -56k + 7k2 = 0 Factor out the Greatest Common Factor (GCF), '7'. 7(15 + -8k + k2) = 0 Factor a trinomial. 7((3 + -1k)(5 + -1k)) = 0 Ignore the factor 7.Subproblem 1
Set the factor '(3 + -1k)' equal to zero and attempt to solve: Simplifying 3 + -1k = 0 Solving 3 + -1k = 0 Move all terms containing k to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1k = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1k = 0 + -3 -1k = 0 + -3 Combine like terms: 0 + -3 = -3 -1k = -3 Divide each side by '-1'. k = 3 Simplifying k = 3Subproblem 2
Set the factor '(5 + -1k)' equal to zero and attempt to solve: Simplifying 5 + -1k = 0 Solving 5 + -1k = 0 Move all terms containing k to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1k = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1k = 0 + -5 -1k = 0 + -5 Combine like terms: 0 + -5 = -5 -1k = -5 Divide each side by '-1'. k = 5 Simplifying k = 5Solution
k = {3, 5}
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