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t^{2}-8t+16=\left(t+4\right)^{2}+32
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(t-4\right)^{2}.
t^{2}-8t+16=t^{2}+8t+16+32
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(t+4\right)^{2}.
t^{2}-8t+16=t^{2}+8t+48
Add 16 and 32 to get 48.
t^{2}-8t+16-t^{2}=8t+48
Subtract t^{2} from both sides.
-8t+16=8t+48
Combine t^{2} and -t^{2} to get 0.
-8t+16-8t=48
Subtract 8t from both sides.
-16t+16=48
Combine -8t and -8t to get -16t.
-16t=48-16
Subtract 16 from both sides.
-16t=32
Subtract 16 from 48 to get 32.
t=\frac{32}{-16}
Divide both sides by -16.
t=-2
Divide 32 by -16 to get -2.