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Simplifying -5 = 2k2 + -7k Reorder the terms: -5 = -7k + 2k2 Solving -5 = -7k + 2k2 Solving for variable 'k'. Reorder the terms: -5 + 7k + -2k2 = -7k + 7k + 2k2 + -2k2 Combine like terms: -7k + 7k = 0 -5 + 7k + -2k2 = 0 + 2k2 + -2k2 -5 + 7k + -2k2 = 2k2 + -2k2 Combine like terms: 2k2 + -2k2 = 0 -5 + 7k + -2k2 = 0 Factor a trinomial. (-5 + 2k)(1 + -1k) = 0Subproblem 1
Set the factor '(-5 + 2k)' equal to zero and attempt to solve: Simplifying -5 + 2k = 0 Solving -5 + 2k = 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 + 2k = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 2k = 0 + 5 2k = 0 + 5 Combine like terms: 0 + 5 = 5 2k = 5 Divide each side by '2'. k = 2.5 Simplifying k = 2.5Subproblem 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 = {2.5, 1}
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