How do you solve #x^2 - 4x +13 = 0 #?
This equation has no solutions
To solve this equation, rather than the classic formula, completing the square may come in handy.
Completing the square means that we can try to find a binomial square "hidden" in the equation and isolate it, and then deal with the rest.
The formula for the square of a binomial is the following:
So, we need two squares, and a third terms, which is twice the multiplication of the bases of the squares.
Your equation starts with
Your equation differs this expression for a difference of
From this point, we are able to tell that the equation has no solution: we want
to be zero, but since a square is always positive, how can a sum of two positive quantities be zero? In other terms, you would have
and again, a square can't be equal to a negative number.