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Simplifying 0 = k2 + -12k + 11 Reorder the terms: 0 = 11 + -12k + k2 Solving 0 = 11 + -12k + k2 Solving for variable 'k'. Combine like terms: 0 + -11 = -11 -11 + 12k + -1k2 = 11 + -12k + k2 + -11 + 12k + -1k2 Reorder the terms: -11 + 12k + -1k2 = 11 + -11 + -12k + 12k + k2 + -1k2 Combine like terms: 11 + -11 = 0 -11 + 12k + -1k2 = 0 + -12k + 12k + k2 + -1k2 -11 + 12k + -1k2 = -12k + 12k + k2 + -1k2 Combine like terms: -12k + 12k = 0 -11 + 12k + -1k2 = 0 + k2 + -1k2 -11 + 12k + -1k2 = k2 + -1k2 Combine like terms: k2 + -1k2 = 0 -11 + 12k + -1k2 = 0 Factor a trinomial. (-11 + k)(1 + -1k) = 0Subproblem 1
Set the factor '(-11 + k)' equal to zero and attempt to solve: Simplifying -11 + k = 0 Solving -11 + k = 0 Move all terms containing k to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + k = 0 + 11 Combine like terms: -11 + 11 = 0 0 + k = 0 + 11 k = 0 + 11 Combine like terms: 0 + 11 = 11 k = 11 Simplifying k = 11Subproblem 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 = {11, 1}
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