Solve for t
t=\frac{k^{2}-6}{2}
k\leq 0
Solve for k
k=-\sqrt{2\left(t+3\right)}
t\geq -3
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2t+6=k^{2}
Square both sides of the equation.
2t+6-6=k^{2}-6
Subtract 6 from both sides of the equation.
2t=k^{2}-6
Subtracting 6 from itself leaves 0.
\frac{2t}{2}=\frac{k^{2}-6}{2}
Divide both sides by 2.
t=\frac{k^{2}-6}{2}
Dividing by 2 undoes the multiplication by 2.
t=\frac{k^{2}}{2}-3
Divide k^{2}-6 by 2.
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