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Simplifying 4k2 + 7 = -11k Reorder the terms: 7 + 4k2 = -11k Solving 7 + 4k2 = -11k Solving for variable 'k'. Reorder the terms: 7 + 11k + 4k2 = -11k + 11k Combine like terms: -11k + 11k = 0 7 + 11k + 4k2 = 0 Factor a trinomial. (7 + 4k)(1 + k) = 0Subproblem 1
Set the factor '(7 + 4k)' equal to zero and attempt to solve: Simplifying 7 + 4k = 0 Solving 7 + 4k = 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 + 4k = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 4k = 0 + -7 4k = 0 + -7 Combine like terms: 0 + -7 = -7 4k = -7 Divide each side by '4'. k = -1.75 Simplifying k = -1.75Subproblem 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 = {-1.75, -1}
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