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Simplifying 24k2 + -45k + 14 = -1k2 Reorder the terms: 14 + -45k + 24k2 = -1k2 Solving 14 + -45k + 24k2 = -1k2 Solving for variable 'k'. Combine like terms: 24k2 + k2 = 25k2 14 + -45k + 25k2 = -1k2 + k2 Combine like terms: -1k2 + k2 = 0 14 + -45k + 25k2 = 0 Factor a trinomial. (2 + -5k)(7 + -5k) = 0Subproblem 1
Set the factor '(2 + -5k)' equal to zero and attempt to solve: Simplifying 2 + -5k = 0 Solving 2 + -5k = 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 + -5k = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -5k = 0 + -2 -5k = 0 + -2 Combine like terms: 0 + -2 = -2 -5k = -2 Divide each side by '-5'. k = 0.4 Simplifying k = 0.4Subproblem 2
Set the factor '(7 + -5k)' equal to zero and attempt to solve: Simplifying 7 + -5k = 0 Solving 7 + -5k = 0 Move all terms containing k to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -5k = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -5k = 0 + -7 -5k = 0 + -7 Combine like terms: 0 + -7 = -7 -5k = -7 Divide each side by '-5'. k = 1.4 Simplifying k = 1.4Solution
k = {0.4, 1.4}
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