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Simplifying (5k + -7)(k + -2) = 0 Reorder the terms: (-7 + 5k)(k + -2) = 0 Reorder the terms: (-7 + 5k)(-2 + k) = 0 Multiply (-7 + 5k) * (-2 + k) (-7(-2 + k) + 5k * (-2 + k)) = 0 ((-2 * -7 + k * -7) + 5k * (-2 + k)) = 0 ((14 + -7k) + 5k * (-2 + k)) = 0 (14 + -7k + (-2 * 5k + k * 5k)) = 0 (14 + -7k + (-10k + 5k2)) = 0 Combine like terms: -7k + -10k = -17k (14 + -17k + 5k2) = 0 Solving 14 + -17k + 5k2 = 0 Solving for variable 'k'. Factor a trinomial. (7 + -5k)(2 + -1k) = 0Subproblem 1
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 = 1.4Subproblem 2
Set the factor '(2 + -1k)' equal to zero and attempt to solve: Simplifying 2 + -1k = 0 Solving 2 + -1k = 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 + -1k = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1k = 0 + -2 -1k = 0 + -2 Combine like terms: 0 + -2 = -2 -1k = -2 Divide each side by '-1'. k = 2 Simplifying k = 2Solution
k = {1.4, 2}
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