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Simplifying 0 = 6k(k) + -11k + -7 Multiply k * k 0 = 6k2 + -11k + -7 Reorder the terms: 0 = -7 + -11k + 6k2 Solving 0 = -7 + -11k + 6k2 Solving for variable 'k'. Combine like terms: 0 + 7 = 7 7 + 11k + -6k2 = -7 + -11k + 6k2 + 7 + 11k + -6k2 Reorder the terms: 7 + 11k + -6k2 = -7 + 7 + -11k + 11k + 6k2 + -6k2 Combine like terms: -7 + 7 = 0 7 + 11k + -6k2 = 0 + -11k + 11k + 6k2 + -6k2 7 + 11k + -6k2 = -11k + 11k + 6k2 + -6k2 Combine like terms: -11k + 11k = 0 7 + 11k + -6k2 = 0 + 6k2 + -6k2 7 + 11k + -6k2 = 6k2 + -6k2 Combine like terms: 6k2 + -6k2 = 0 7 + 11k + -6k2 = 0 Factor a trinomial. (7 + -3k)(1 + 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 '(1 + 2k)' equal to zero and attempt to solve: Simplifying 1 + 2k = 0 Solving 1 + 2k = 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 + 2k = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2k = 0 + -1 2k = 0 + -1 Combine like terms: 0 + -1 = -1 2k = -1 Divide each side by '2'. k = -0.5 Simplifying k = -0.5Solution
k = {2.333333333, -0.5}
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