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Simplifying 3k2 + k + -3 = 7 Reorder the terms: -3 + k + 3k2 = 7 Solving -3 + k + 3k2 = 7 Solving for variable 'k'. Reorder the terms: -3 + -7 + k + 3k2 = 7 + -7 Combine like terms: -3 + -7 = -10 -10 + k + 3k2 = 7 + -7 Combine like terms: 7 + -7 = 0 -10 + k + 3k2 = 0 Factor a trinomial. (-2 + -1k)(5 + -3k) = 0Subproblem 1
Set the factor '(-2 + -1k)' equal to zero and attempt to solve: Simplifying -2 + -1k = 0 Solving -2 + -1k = 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 + -1k = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1k = 0 + 2 -1k = 0 + 2 Combine like terms: 0 + 2 = 2 -1k = 2 Divide each side by '-1'. k = -2 Simplifying k = -2Subproblem 2
Set the factor '(5 + -3k)' equal to zero and attempt to solve: Simplifying 5 + -3k = 0 Solving 5 + -3k = 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 + -3k = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -3k = 0 + -5 -3k = 0 + -5 Combine like terms: 0 + -5 = -5 -3k = -5 Divide each side by '-3'. k = 1.666666667 Simplifying k = 1.666666667Solution
k = {-2, 1.666666667}
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