# Solving Equations then tell which solution method you used!

G

#### Guest

##### Guest
T^2 -16T +65=0

I've tried the Quadratic formula
Factoring and Graphin but 65 only factors are
1 *65 and
5*13???
Any one have any ideas??? Please??? Mom's lost...and My son had left this problem after working on it for over an hour! Thanks Mom :?

#### royhaas

##### Full Member
The quadratic formula works. The solution will be two conjugate complex numbers.

G

#### Guest

##### Guest
Lost

when I use the formula I come up with a negative 4 in the aquare root which can't be so I get only 16 +/- 0 divided by 2 which gives me only 8 as an answer????

#### royhaas

##### Full Member
The square root of a negative number is a complex number, sometimes called an imaginary number. You write it as $$\displaystyle \sqrt{-4}=2i$$, where $$\displaystyle i^2 = -1$$. So one root will have $$\displaystyle +2i$$ and the other will have $$\displaystyle \ -2i$$ as part of the solution. In other words,
$$\displaystyle x = 8+i, x=8-i$$ is the solution.

The check is that $$\displaystyle (x-8-i)(x-8+i)=(x-8)^2-i^2 = x^2-16x+64+1$$.