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Simplifying 5k2 = 34k + 7 Reorder the terms: 5k2 = 7 + 34k Solving 5k2 = 7 + 34k Solving for variable 'k'. Reorder the terms: -7 + -34k + 5k2 = 7 + 34k + -7 + -34k Reorder the terms: -7 + -34k + 5k2 = 7 + -7 + 34k + -34k Combine like terms: 7 + -7 = 0 -7 + -34k + 5k2 = 0 + 34k + -34k -7 + -34k + 5k2 = 34k + -34k Combine like terms: 34k + -34k = 0 -7 + -34k + 5k2 = 0 Factor a trinomial. (-1 + -5k)(7 + -1k) = 0Subproblem 1
Set the factor '(-1 + -5k)' equal to zero and attempt to solve: Simplifying -1 + -5k = 0 Solving -1 + -5k = 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 + -5k = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -5k = 0 + 1 -5k = 0 + 1 Combine like terms: 0 + 1 = 1 -5k = 1 Divide each side by '-5'. k = -0.2 Simplifying k = -0.2Subproblem 2
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 = 7Solution
k = {-0.2, 7}
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