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Simplifying (2k + -1)(k + 7) = 0 Reorder the terms: (-1 + 2k)(k + 7) = 0 Reorder the terms: (-1 + 2k)(7 + k) = 0 Multiply (-1 + 2k) * (7 + k) (-1(7 + k) + 2k * (7 + k)) = 0 ((7 * -1 + k * -1) + 2k * (7 + k)) = 0 ((-7 + -1k) + 2k * (7 + k)) = 0 (-7 + -1k + (7 * 2k + k * 2k)) = 0 (-7 + -1k + (14k + 2k2)) = 0 Combine like terms: -1k + 14k = 13k (-7 + 13k + 2k2) = 0 Solving -7 + 13k + 2k2 = 0 Solving for variable 'k'. Factor a trinomial. (-7 + -1k)(1 + -2k) = 0Subproblem 1
Set the factor '(-7 + -1k)' equal to zero and attempt to solve: Simplifying -7 + -1k = 0 Solving -7 + -1k = 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 + -1k = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -1k = 0 + 7 -1k = 0 + 7 Combine like terms: 0 + 7 = 7 -1k = 7 Divide each side by '-1'. k = -7 Simplifying k = -7Subproblem 2
Set the factor '(1 + -2k)' equal to zero and attempt to solve: Simplifying 1 + -2k = 0 Solving 1 + -2k = 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 + -2k = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2k = 0 + -1 -2k = 0 + -1 Combine like terms: 0 + -1 = -1 -2k = -1 Divide each side by '-2'. k = 0.5 Simplifying k = 0.5Solution
k = {-7, 0.5}
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