# How do you solve #x^2-3x+3=0# by completing the square?

##### 1 Answer

For

Divide through by the coefficient of

Move the constant to the right hand side.

Add to both sides the square of half the coefficient of

The square of half the coefficient in this case is

So we have:

Convert

We now have :

Collect terms on right hand side:

Taking roots of both sides:

Factoring inside the radical:

where

taking any exact roots and simplifying:

Note:

If this is your first time solving quadratics by completion of the square, it would have been best to choose an equation that had real rather than imaginary roots. This would have been easier to start of with.