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Simplifying (5k2 + -8 + 2k) + (7k2 + -6k + 3) = 0 Reorder the terms: (-8 + 2k + 5k2) + (7k2 + -6k + 3) = 0 Remove parenthesis around (-8 + 2k + 5k2) -8 + 2k + 5k2 + (7k2 + -6k + 3) = 0 Reorder the terms: -8 + 2k + 5k2 + (3 + -6k + 7k2) = 0 Remove parenthesis around (3 + -6k + 7k2) -8 + 2k + 5k2 + 3 + -6k + 7k2 = 0 Reorder the terms: -8 + 3 + 2k + -6k + 5k2 + 7k2 = 0 Combine like terms: -8 + 3 = -5 -5 + 2k + -6k + 5k2 + 7k2 = 0 Combine like terms: 2k + -6k = -4k -5 + -4k + 5k2 + 7k2 = 0 Combine like terms: 5k2 + 7k2 = 12k2 -5 + -4k + 12k2 = 0 Solving -5 + -4k + 12k2 = 0 Solving for variable 'k'. Factor a trinomial. (-1 + -2k)(5 + -6k) = 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 + -6k)' equal to zero and attempt to solve: Simplifying 5 + -6k = 0 Solving 5 + -6k = 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 + -6k = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -6k = 0 + -5 -6k = 0 + -5 Combine like terms: 0 + -5 = -5 -6k = -5 Divide each side by '-6'. k = 0.8333333333 Simplifying k = 0.8333333333Solution
k = {-0.5, 0.8333333333}
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