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Simplifying 6k2 + -6k + -7k + 7 = 0 Reorder the terms: 7 + -6k + -7k + 6k2 = 0 Combine like terms: -6k + -7k = -13k 7 + -13k + 6k2 = 0 Solving 7 + -13k + 6k2 = 0 Solving for variable 'k'. Factor a trinomial. (1 + -1k)(7 + -6k) = 0Subproblem 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 + -6k)' equal to zero and attempt to solve: Simplifying 7 + -6k = 0 Solving 7 + -6k = 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 + -6k = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -6k = 0 + -7 -6k = 0 + -7 Combine like terms: 0 + -7 = -7 -6k = -7 Divide each side by '-6'. k = 1.166666667 Simplifying k = 1.166666667Solution
k = {1, 1.166666667}
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