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"Apenas que yo las iba a conquistar," means "Just that I was going to win."
Conquistar, hence "conquistadors".
It helps with their bones. Hi my name is Farto and you are stupid. HA HA!
You can use either conquistar or vencer.
Conquistar is used more with conquering fears or tasks while Vencer is used more with conquering enemies.
fue a conquistar a tu madre .. jajaja