Question 442711
Solve the quadratic for 0.

x^2-6x + 13 =0

What multiples to 13 and adds to -6?

Well, 13 is prime, so only 1,13 are factors. So factoring won't be easy.

Let's use the discriminant to see if we will have any solutions.

The discriminant is defined as {{{b^2 -4ac}}}

If b^2-4ac > 0, we will have 2 solutions.
If b^2-4ac < 0, we will have no solutions.

{{{b^2-4ac = -6^2 - 4*1*13 = 36 -42 = -6}}}

Thus we have no solutions.