why is it called quadratic formula? [duplicate]

why is the quadratic formula called the quadratic formula when quad means four and x is only to the power of two and there are only three terms and you can use it more than four times.

this is very concerning.

• @H.sapiensrex I am pretty sure the verb "quadrare" and the number "quattuor" are themselves etymologically related.
– Ian
Commented May 21 at 22:53
• @Arthur im just guessing, but perhaps it has to do with how the formula is derived by completing the square? Commented May 21 at 22:56

Historically, quadratic equations were viewed as equalities about areas of squares and rectangles. They were even treated differently depending on what we now call the signs of the coefficients. For example, $$x^2=bx+c$$ for $$b,c>0$$ was analyzed separately from $$x^2+bx=c$$ for $$b,c>0$$. That central role of squares and rectangles is the etymology of the word "quadratic"; indeed "quadrum" means "square" and "quadratum" means "having been made square" in Latin. These are both more distantly related to the word "quattuor" meaning "four".