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Simplifying 5k2 + -35 = 30k Reorder the terms: -35 + 5k2 = 30k Solving -35 + 5k2 = 30k Solving for variable 'k'. Reorder the terms: -35 + -30k + 5k2 = 30k + -30k Combine like terms: 30k + -30k = 0 -35 + -30k + 5k2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-7 + -6k + k2) = 0 Factor a trinomial. 5((-1 + -1k)(7 + -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 '(7 + -1k)' equal to zero and attempt to solve: Simplifying 7 + -1k = 0 Solving 7 + -1k = 0 Move all terms containing k to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1k = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1k = 0 + -7 -1k = 0 + -7 Combine like terms: 0 + -7 = -7 -1k = -7 Divide each side by '-1'. k = 7 Simplifying k = 7Solution
k = {-1, 7}
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