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Simplifying 7k = 2k2 + -9 Reorder the terms: 7k = -9 + 2k2 Solving 7k = -9 + 2k2 Solving for variable 'k'. Reorder the terms: 9 + 7k + -2k2 = -9 + 2k2 + 9 + -2k2 Reorder the terms: 9 + 7k + -2k2 = -9 + 9 + 2k2 + -2k2 Combine like terms: -9 + 9 = 0 9 + 7k + -2k2 = 0 + 2k2 + -2k2 9 + 7k + -2k2 = 2k2 + -2k2 Combine like terms: 2k2 + -2k2 = 0 9 + 7k + -2k2 = 0 Factor a trinomial. (9 + -2k)(1 + k) = 0Subproblem 1
Set the factor '(9 + -2k)' equal to zero and attempt to solve: Simplifying 9 + -2k = 0 Solving 9 + -2k = 0 Move all terms containing k to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -2k = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -2k = 0 + -9 -2k = 0 + -9 Combine like terms: 0 + -9 = -9 -2k = -9 Divide each side by '-2'. k = 4.5 Simplifying k = 4.5Subproblem 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 = {4.5, -1}
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