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Simplifying -1k2 + -4k + 4 = -4k2 + 3k Reorder the terms: 4 + -4k + -1k2 = -4k2 + 3k Reorder the terms: 4 + -4k + -1k2 = 3k + -4k2 Solving 4 + -4k + -1k2 = 3k + -4k2 Solving for variable 'k'. Reorder the terms: 4 + -4k + -3k + -1k2 + 4k2 = 3k + -4k2 + -3k + 4k2 Combine like terms: -4k + -3k = -7k 4 + -7k + -1k2 + 4k2 = 3k + -4k2 + -3k + 4k2 Combine like terms: -1k2 + 4k2 = 3k2 4 + -7k + 3k2 = 3k + -4k2 + -3k + 4k2 Reorder the terms: 4 + -7k + 3k2 = 3k + -3k + -4k2 + 4k2 Combine like terms: 3k + -3k = 0 4 + -7k + 3k2 = 0 + -4k2 + 4k2 4 + -7k + 3k2 = -4k2 + 4k2 Combine like terms: -4k2 + 4k2 = 0 4 + -7k + 3k2 = 0 Factor a trinomial. (1 + -1k)(4 + -3k) = 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 '(4 + -3k)' equal to zero and attempt to solve: Simplifying 4 + -3k = 0 Solving 4 + -3k = 0 Move all terms containing k to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -3k = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -3k = 0 + -4 -3k = 0 + -4 Combine like terms: 0 + -4 = -4 -3k = -4 Divide each side by '-3'. k = 1.333333333 Simplifying k = 1.333333333Solution
k = {1, 1.333333333}
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