How do you solve #x^2=12x-45# by completing the square?
Start by getting the
Now you need to focus on writing the left side of the equation as a square of a binomial by adding a term to both sides of the equation.
The coefficient of the
This means that you must add
The left side of the equation can now be written as
The equation becomes
You can tell right away that this equation has no real solutions, so you're going to have to use complex numbers to get the solutions you want.
Take the square root of both sides to get
Now, the square root of a negative number can be written, using the fact that
In your case, you have
The two solutions to your quadratic will thus be