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Simplifying 6k2 = 35 + k Solving 6k2 = 35 + k Solving for variable 'k'. Reorder the terms: -35 + -1k + 6k2 = 35 + k + -35 + -1k Reorder the terms: -35 + -1k + 6k2 = 35 + -35 + k + -1k Combine like terms: 35 + -35 = 0 -35 + -1k + 6k2 = 0 + k + -1k -35 + -1k + 6k2 = k + -1k Combine like terms: k + -1k = 0 -35 + -1k + 6k2 = 0 Factor a trinomial. (-7 + -3k)(5 + -2k) = 0Subproblem 1
Set the factor '(-7 + -3k)' equal to zero and attempt to solve: Simplifying -7 + -3k = 0 Solving -7 + -3k = 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 + -3k = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -3k = 0 + 7 -3k = 0 + 7 Combine like terms: 0 + 7 = 7 -3k = 7 Divide each side by '-3'. k = -2.333333333 Simplifying k = -2.333333333Subproblem 2
Set the factor '(5 + -2k)' equal to zero and attempt to solve: Simplifying 5 + -2k = 0 Solving 5 + -2k = 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 + -2k = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2k = 0 + -5 -2k = 0 + -5 Combine like terms: 0 + -5 = -5 -2k = -5 Divide each side by '-2'. k = 2.5 Simplifying k = 2.5Solution
k = {-2.333333333, 2.5}
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