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Simplifying 5k2 = -25 + 30k Solving 5k2 = -25 + 30k Solving for variable 'k'. Reorder the terms: 25 + -30k + 5k2 = -25 + 30k + 25 + -30k Reorder the terms: 25 + -30k + 5k2 = -25 + 25 + 30k + -30k Combine like terms: -25 + 25 = 0 25 + -30k + 5k2 = 0 + 30k + -30k 25 + -30k + 5k2 = 30k + -30k Combine like terms: 30k + -30k = 0 25 + -30k + 5k2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(5 + -6k + k2) = 0 Factor a trinomial. 5((1 + -1k)(5 + -1k)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(1 + -1k)' equal to zero and attempt to solve: Simplifying 1 + -1k = 0 Solving 1 + -1k = 0 Move all terms containing k to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1k = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1k = 0 + -1 -1k = 0 + -1 Combine like terms: 0 + -1 = -1 -1k = -1 Divide each side by '-1'. k = 1 Simplifying k = 1Subproblem 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 = {1, 5}
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