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Simplifying 0 = 4k2 + -5k + -21 Reorder the terms: 0 = -21 + -5k + 4k2 Solving 0 = -21 + -5k + 4k2 Solving for variable 'k'. Combine like terms: 0 + 21 = 21 21 + 5k + -4k2 = -21 + -5k + 4k2 + 21 + 5k + -4k2 Reorder the terms: 21 + 5k + -4k2 = -21 + 21 + -5k + 5k + 4k2 + -4k2 Combine like terms: -21 + 21 = 0 21 + 5k + -4k2 = 0 + -5k + 5k + 4k2 + -4k2 21 + 5k + -4k2 = -5k + 5k + 4k2 + -4k2 Combine like terms: -5k + 5k = 0 21 + 5k + -4k2 = 0 + 4k2 + -4k2 21 + 5k + -4k2 = 4k2 + -4k2 Combine like terms: 4k2 + -4k2 = 0 21 + 5k + -4k2 = 0 Factor a trinomial. (3 + -1k)(7 + 4k) = 0Subproblem 1
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 = 3Subproblem 2
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 = -1.75Solution
k = {3, -1.75}
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