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Simplifying 9k2 + 30k + 25 = 36 Reorder the terms: 25 + 30k + 9k2 = 36 Solving 25 + 30k + 9k2 = 36 Solving for variable 'k'. Reorder the terms: 25 + -36 + 30k + 9k2 = 36 + -36 Combine like terms: 25 + -36 = -11 -11 + 30k + 9k2 = 36 + -36 Combine like terms: 36 + -36 = 0 -11 + 30k + 9k2 = 0 Factor a trinomial. (-11 + -3k)(1 + -3k) = 0Subproblem 1
Set the factor '(-11 + -3k)' equal to zero and attempt to solve: Simplifying -11 + -3k = 0 Solving -11 + -3k = 0 Move all terms containing k to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + -3k = 0 + 11 Combine like terms: -11 + 11 = 0 0 + -3k = 0 + 11 -3k = 0 + 11 Combine like terms: 0 + 11 = 11 -3k = 11 Divide each side by '-3'. k = -3.666666667 Simplifying k = -3.666666667Subproblem 2
Set the factor '(1 + -3k)' equal to zero and attempt to solve: Simplifying 1 + -3k = 0 Solving 1 + -3k = 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 + -3k = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3k = 0 + -1 -3k = 0 + -1 Combine like terms: 0 + -1 = -1 -3k = -1 Divide each side by '-3'. k = 0.3333333333 Simplifying k = 0.3333333333Solution
k = {-3.666666667, 0.3333333333}
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