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Simplifying 68k = 72 + -4k2 Solving 68k = 72 + -4k2 Solving for variable 'k'. Reorder the terms: -72 + 68k + 4k2 = 72 + -4k2 + -72 + 4k2 Reorder the terms: -72 + 68k + 4k2 = 72 + -72 + -4k2 + 4k2 Combine like terms: 72 + -72 = 0 -72 + 68k + 4k2 = 0 + -4k2 + 4k2 -72 + 68k + 4k2 = -4k2 + 4k2 Combine like terms: -4k2 + 4k2 = 0 -72 + 68k + 4k2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-18 + 17k + k2) = 0 Factor a trinomial. 4((-18 + -1k)(1 + -1k)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-18 + -1k)' equal to zero and attempt to solve: Simplifying -18 + -1k = 0 Solving -18 + -1k = 0 Move all terms containing k to the left, all other terms to the right. Add '18' to each side of the equation. -18 + 18 + -1k = 0 + 18 Combine like terms: -18 + 18 = 0 0 + -1k = 0 + 18 -1k = 0 + 18 Combine like terms: 0 + 18 = 18 -1k = 18 Divide each side by '-1'. k = -18 Simplifying k = -18Subproblem 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 = {-18, 1}
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