Solve for k
k=-\frac{2}{a_{0}-2}
a_{0}\neq 2
Solve for a_0
a_{0}=2-\frac{2}{k}
k\neq 0
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a_{0}k=2k-2
Variable k cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by k.
a_{0}k-2k=-2
Subtract 2k from both sides.
\left(a_{0}-2\right)k=-2
Combine all terms containing k.
\frac{\left(a_{0}-2\right)k}{a_{0}-2}=-\frac{2}{a_{0}-2}
Divide both sides by a_{0}-2.
k=-\frac{2}{a_{0}-2}
Dividing by a_{0}-2 undoes the multiplication by a_{0}-2.
k=-\frac{2}{a_{0}-2}\text{, }k\neq 0
Variable k cannot be equal to 0.
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