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Simplifying 2k2 = 7 + -5k Solving 2k2 = 7 + -5k Solving for variable 'k'. Reorder the terms: -7 + 5k + 2k2 = 7 + -5k + -7 + 5k Reorder the terms: -7 + 5k + 2k2 = 7 + -7 + -5k + 5k Combine like terms: 7 + -7 = 0 -7 + 5k + 2k2 = 0 + -5k + 5k -7 + 5k + 2k2 = -5k + 5k Combine like terms: -5k + 5k = 0 -7 + 5k + 2k2 = 0 Factor a trinomial. (-7 + -2k)(1 + -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 '(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 = {-3.5, 1}
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