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Simplifying 3k2 = 14 + -19k Solving 3k2 = 14 + -19k Solving for variable 'k'. Reorder the terms: -14 + 19k + 3k2 = 14 + -19k + -14 + 19k Reorder the terms: -14 + 19k + 3k2 = 14 + -14 + -19k + 19k Combine like terms: 14 + -14 = 0 -14 + 19k + 3k2 = 0 + -19k + 19k -14 + 19k + 3k2 = -19k + 19k Combine like terms: -19k + 19k = 0 -14 + 19k + 3k2 = 0 Factor a trinomial. (-7 + -1k)(2 + -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 '(2 + -3k)' equal to zero and attempt to solve: Simplifying 2 + -3k = 0 Solving 2 + -3k = 0 Move all terms containing k to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -3k = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3k = 0 + -2 -3k = 0 + -2 Combine like terms: 0 + -2 = -2 -3k = -2 Divide each side by '-3'. k = 0.6666666667 Simplifying k = 0.6666666667Solution
k = {-7, 0.6666666667}
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