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Simplifying 5k2 = 12 + -7k Solving 5k2 = 12 + -7k Solving for variable 'k'. Reorder the terms: -12 + 7k + 5k2 = 12 + -7k + -12 + 7k Reorder the terms: -12 + 7k + 5k2 = 12 + -12 + -7k + 7k Combine like terms: 12 + -12 = 0 -12 + 7k + 5k2 = 0 + -7k + 7k -12 + 7k + 5k2 = -7k + 7k Combine like terms: -7k + 7k = 0 -12 + 7k + 5k2 = 0 Factor a trinomial. (-12 + -5k)(1 + -1k) = 0Subproblem 1
Set the factor '(-12 + -5k)' equal to zero and attempt to solve: Simplifying -12 + -5k = 0 Solving -12 + -5k = 0 Move all terms containing k to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + -5k = 0 + 12 Combine like terms: -12 + 12 = 0 0 + -5k = 0 + 12 -5k = 0 + 12 Combine like terms: 0 + 12 = 12 -5k = 12 Divide each side by '-5'. k = -2.4 Simplifying k = -2.4Subproblem 2
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 = 1Solution
k = {-2.4, 1}
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