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Simplifying 2k2 = 49 + 7k Solving 2k2 = 49 + 7k Solving for variable 'k'. Reorder the terms: -49 + -7k + 2k2 = 49 + 7k + -49 + -7k Reorder the terms: -49 + -7k + 2k2 = 49 + -49 + 7k + -7k Combine like terms: 49 + -49 = 0 -49 + -7k + 2k2 = 0 + 7k + -7k -49 + -7k + 2k2 = 7k + -7k Combine like terms: 7k + -7k = 0 -49 + -7k + 2k2 = 0 Factor a trinomial. (-7 + -2k)(7 + -1k) = 0Subproblem 1
Set the factor '(-7 + -2k)' equal to zero and attempt to solve: Simplifying -7 + -2k = 0 Solving -7 + -2k = 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 + -2k = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -2k = 0 + 7 -2k = 0 + 7 Combine like terms: 0 + 7 = 7 -2k = 7 Divide each side by '-2'. k = -3.5 Simplifying k = -3.5Subproblem 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 = {-3.5, 7}
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