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Simplifying 4k2 + -4k + -38 = -3 Reorder the terms: -38 + -4k + 4k2 = -3 Solving -38 + -4k + 4k2 = -3 Solving for variable 'k'. Reorder the terms: -38 + 3 + -4k + 4k2 = -3 + 3 Combine like terms: -38 + 3 = -35 -35 + -4k + 4k2 = -3 + 3 Combine like terms: -3 + 3 = 0 -35 + -4k + 4k2 = 0 Factor a trinomial. (-5 + -2k)(7 + -2k) = 0Subproblem 1
Set the factor '(-5 + -2k)' equal to zero and attempt to solve: Simplifying -5 + -2k = 0 Solving -5 + -2k = 0 Move all terms containing k to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -2k = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -2k = 0 + 5 -2k = 0 + 5 Combine like terms: 0 + 5 = 5 -2k = 5 Divide each side by '-2'. k = -2.5 Simplifying k = -2.5Subproblem 2
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 = 3.5Solution
k = {-2.5, 3.5}
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