How do you solve #x^2 - 5x + 1 = 0# by completing the square?
Starting from the general form of the quadratic equation
get your quadratic to the form
In your case,
Now, in order to solve this equation by completing the square, you need to find a term to add to both sides of the equation such that the left side of the equation can be written as the square of a binomial.
The coefficient of the
So, divide this coefficient by 2, then square the result. In your case, you have
This means that the quadratic becomes
Using the formula for the square of a binomial
the left side of the equation can now be written as
Your quadratic is now equivalent to
Take the square root of both sides to get
The two solutions to this equation will be