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Simplifying k2 + -4k + 10 = 7 Reorder the terms: 10 + -4k + k2 = 7 Solving 10 + -4k + k2 = 7 Solving for variable 'k'. Reorder the terms: 10 + -7 + -4k + k2 = 7 + -7 Combine like terms: 10 + -7 = 3 3 + -4k + k2 = 7 + -7 Combine like terms: 7 + -7 = 0 3 + -4k + k2 = 0 Factor a trinomial. (1 + -1k)(3 + -1k) = 0Subproblem 1
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 = 1Subproblem 2
Set the factor '(3 + -1k)' equal to zero and attempt to solve: Simplifying 3 + -1k = 0 Solving 3 + -1k = 0 Move all terms containing k to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1k = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1k = 0 + -3 -1k = 0 + -3 Combine like terms: 0 + -3 = -3 -1k = -3 Divide each side by '-1'. k = 3 Simplifying k = 3Solution
k = {1, 3}
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