I have this problem to solve. It's been a while since I tried to figured out how to do, but I am totally lost.
Here it is.
Prove SST= SSW+SST in one-way Anova (one factor).
Σ ( xi - x̄ )² = Σ (xi - x̄ + x̄ k - x̄ k ) ²
Hint: Σ [ ( xi - x̄ k ) + ( x̄ k - x̄ )]²