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Simplifying 5k2 = 3k + 8 Reorder the terms: 5k2 = 8 + 3k Solving 5k2 = 8 + 3k Solving for variable 'k'. Reorder the terms: -8 + -3k + 5k2 = 8 + 3k + -8 + -3k Reorder the terms: -8 + -3k + 5k2 = 8 + -8 + 3k + -3k Combine like terms: 8 + -8 = 0 -8 + -3k + 5k2 = 0 + 3k + -3k -8 + -3k + 5k2 = 3k + -3k Combine like terms: 3k + -3k = 0 -8 + -3k + 5k2 = 0 Factor a trinomial. (-1 + -1k)(8 + -5k) = 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 '(8 + -5k)' equal to zero and attempt to solve: Simplifying 8 + -5k = 0 Solving 8 + -5k = 0 Move all terms containing k to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -5k = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -5k = 0 + -8 -5k = 0 + -8 Combine like terms: 0 + -8 = -8 -5k = -8 Divide each side by '-5'. k = 1.6 Simplifying k = 1.6Solution
k = {-1, 1.6}
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