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Simplifying (5 + 3k) + (3 + -5k2) = 0 Remove parenthesis around (5 + 3k) 5 + 3k + (3 + -5k2) = 0 Remove parenthesis around (3 + -5k2) 5 + 3k + 3 + -5k2 = 0 Reorder the terms: 5 + 3 + 3k + -5k2 = 0 Combine like terms: 5 + 3 = 8 8 + 3k + -5k2 = 0 Solving 8 + 3k + -5k2 = 0 Solving for variable 'k'. Factor a trinomial. (8 + -5k)(1 + k) = 0Subproblem 1
Set the factor '(8 + -5k)' equal to zero and attempt to solve: Simplifying 8 + -5k = 0 Solving 8 + -5k = 0 Move all terms containing k to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -5k = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -5k = 0 + -8 -5k = 0 + -8 Combine like terms: 0 + -8 = -8 -5k = -8 Divide each side by '-5'. k = 1.6 Simplifying k = 1.6Subproblem 2
Set the factor '(1 + k)' equal to zero and attempt to solve: Simplifying 1 + k = 0 Solving 1 + k = 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 + k = 0 + -1 Combine like terms: 1 + -1 = 0 0 + k = 0 + -1 k = 0 + -1 Combine like terms: 0 + -1 = -1 k = -1 Simplifying k = -1Solution
k = {1.6, -1}
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