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Simplifying 8k2 = -5 + 14k Solving 8k2 = -5 + 14k Solving for variable 'k'. Reorder the terms: 5 + -14k + 8k2 = -5 + 14k + 5 + -14k Reorder the terms: 5 + -14k + 8k2 = -5 + 5 + 14k + -14k Combine like terms: -5 + 5 = 0 5 + -14k + 8k2 = 0 + 14k + -14k 5 + -14k + 8k2 = 14k + -14k Combine like terms: 14k + -14k = 0 5 + -14k + 8k2 = 0 Factor a trinomial. (1 + -2k)(5 + -4k) = 0Subproblem 1
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 = 0.5Subproblem 2
Set the factor '(5 + -4k)' equal to zero and attempt to solve: Simplifying 5 + -4k = 0 Solving 5 + -4k = 0 Move all terms containing k to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -4k = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -4k = 0 + -5 -4k = 0 + -5 Combine like terms: 0 + -5 = -5 -4k = -5 Divide each side by '-4'. k = 1.25 Simplifying k = 1.25Solution
k = {0.5, 1.25}
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