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Simplifying 3k2 = 77 + -10k Solving 3k2 = 77 + -10k Solving for variable 'k'. Reorder the terms: -77 + 10k + 3k2 = 77 + -10k + -77 + 10k Reorder the terms: -77 + 10k + 3k2 = 77 + -77 + -10k + 10k Combine like terms: 77 + -77 = 0 -77 + 10k + 3k2 = 0 + -10k + 10k -77 + 10k + 3k2 = -10k + 10k Combine like terms: -10k + 10k = 0 -77 + 10k + 3k2 = 0 Factor a trinomial. (-7 + -1k)(11 + -3k) = 0Subproblem 1
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 = -7Subproblem 2
Set the factor '(11 + -3k)' equal to zero and attempt to solve: Simplifying 11 + -3k = 0 Solving 11 + -3k = 0 Move all terms containing k to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + -3k = 0 + -11 Combine like terms: 11 + -11 = 0 0 + -3k = 0 + -11 -3k = 0 + -11 Combine like terms: 0 + -11 = -11 -3k = -11 Divide each side by '-3'. k = 3.666666667 Simplifying k = 3.666666667Solution
k = {-7, 3.666666667}
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