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Simplifying 84k2 + 40k + -64 = 0 Reorder the terms: -64 + 40k + 84k2 = 0 Solving -64 + 40k + 84k2 = 0 Solving for variable 'k'. Factor out the Greatest Common Factor (GCF), '4'. 4(-16 + 10k + 21k2) = 0 Factor a trinomial. 4((-8 + -7k)(2 + -3k)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-8 + -7k)' equal to zero and attempt to solve: Simplifying -8 + -7k = 0 Solving -8 + -7k = 0 Move all terms containing k to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + -7k = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -7k = 0 + 8 -7k = 0 + 8 Combine like terms: 0 + 8 = 8 -7k = 8 Divide each side by '-7'. k = -1.142857143 Simplifying k = -1.142857143Subproblem 2
Set the factor '(2 + -3k)' equal to zero and attempt to solve: Simplifying 2 + -3k = 0 Solving 2 + -3k = 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 + -3k = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3k = 0 + -2 -3k = 0 + -2 Combine like terms: 0 + -2 = -2 -3k = -2 Divide each side by '-3'. k = 0.6666666667 Simplifying k = 0.6666666667Solution
k = {-1.142857143, 0.6666666667}
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