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Simplifying 9k5 = 4k Solving 9k5 = 4k Solving for variable 'k'. Reorder the terms: -4k + 9k5 = 4k + -4k Combine like terms: 4k + -4k = 0 -4k + 9k5 = 0 Factor out the Greatest Common Factor (GCF), 'k'. k(-4 + 9k4) = 0 Factor a difference between two squares. k((2 + 3k2)(-2 + 3k2)) = 0Subproblem 1
Set the factor 'k' equal to zero and attempt to solve: Simplifying k = 0 Solving k = 0 Move all terms containing k to the left, all other terms to the right. Simplifying k = 0Subproblem 2
Set the factor '(2 + 3k2)' equal to zero and attempt to solve: Simplifying 2 + 3k2 = 0 Solving 2 + 3k2 = 0 Move all terms containing k to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + 3k2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 3k2 = 0 + -2 3k2 = 0 + -2 Combine like terms: 0 + -2 = -2 3k2 = -2 Divide each side by '3'. k2 = -0.6666666667 Simplifying k2 = -0.6666666667 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 3
Set the factor '(-2 + 3k2)' equal to zero and attempt to solve: Simplifying -2 + 3k2 = 0 Solving -2 + 3k2 = 0 Move all terms containing k to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + 3k2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 3k2 = 0 + 2 3k2 = 0 + 2 Combine like terms: 0 + 2 = 2 3k2 = 2 Divide each side by '3'. k2 = 0.6666666667 Simplifying k2 = 0.6666666667 Take the square root of each side: k = {-0.816496581, 0.816496581}Solution
k = {0, -0.816496581, 0.816496581}
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