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Simplifying (8k + -7)(k + 1) = 0 Reorder the terms: (-7 + 8k)(k + 1) = 0 Reorder the terms: (-7 + 8k)(1 + k) = 0 Multiply (-7 + 8k) * (1 + k) (-7(1 + k) + 8k * (1 + k)) = 0 ((1 * -7 + k * -7) + 8k * (1 + k)) = 0 ((-7 + -7k) + 8k * (1 + k)) = 0 (-7 + -7k + (1 * 8k + k * 8k)) = 0 (-7 + -7k + (8k + 8k2)) = 0 Combine like terms: -7k + 8k = 1k (-7 + 1k + 8k2) = 0 Solving -7 + 1k + 8k2 = 0 Solving for variable 'k'. Factor a trinomial. (-1 + -1k)(7 + -8k) = 0Subproblem 1
Set the factor '(-1 + -1k)' equal to zero and attempt to solve: Simplifying -1 + -1k = 0 Solving -1 + -1k = 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 + -1k = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1k = 0 + 1 -1k = 0 + 1 Combine like terms: 0 + 1 = 1 -1k = 1 Divide each side by '-1'. k = -1 Simplifying k = -1Subproblem 2
Set the factor '(7 + -8k)' equal to zero and attempt to solve: Simplifying 7 + -8k = 0 Solving 7 + -8k = 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 + -8k = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -8k = 0 + -7 -8k = 0 + -7 Combine like terms: 0 + -7 = -7 -8k = -7 Divide each side by '-8'. k = 0.875 Simplifying k = 0.875Solution
k = {-1, 0.875}
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