An instrument is a concrete or abstract tool intended for a purpose other than mechanical work, in particular a refined one.
Musical instruments are devices designed to produce music, frequently by plucking or striking a string or bell or drum surface, or by forcing air to resonate (see wind instruments).
... To "complete the square" is to add a constant (i.e., in this case, a quantity that does not depend on x) to the expression to the left of "=", that will make it a ...