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Simplifying 4k2 + 9k = 100 Reorder the terms: 9k + 4k2 = 100 Solving 9k + 4k2 = 100 Solving for variable 'k'. Reorder the terms: -100 + 9k + 4k2 = 100 + -100 Combine like terms: 100 + -100 = 0 -100 + 9k + 4k2 = 0 Factor a trinomial. (-25 + -4k)(4 + -1k) = 0Subproblem 1
Set the factor '(-25 + -4k)' equal to zero and attempt to solve: Simplifying -25 + -4k = 0 Solving -25 + -4k = 0 Move all terms containing k to the left, all other terms to the right. Add '25' to each side of the equation. -25 + 25 + -4k = 0 + 25 Combine like terms: -25 + 25 = 0 0 + -4k = 0 + 25 -4k = 0 + 25 Combine like terms: 0 + 25 = 25 -4k = 25 Divide each side by '-4'. k = -6.25 Simplifying k = -6.25Subproblem 2
Set the factor '(4 + -1k)' equal to zero and attempt to solve: Simplifying 4 + -1k = 0 Solving 4 + -1k = 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 + -1k = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1k = 0 + -4 -1k = 0 + -4 Combine like terms: 0 + -4 = -4 -1k = -4 Divide each side by '-1'. k = 4 Simplifying k = 4Solution
k = {-6.25, 4}
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