How do you find the discriminant and how many solutions does $m^2-8m=-14$ have?

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Answer 1 · 2015-05-10T23:43:28

First, add 14 to both sides to get $m^2-8m+14=0$ .

This is in standard form like $am^2+bm+c = 0$ , with $a=1$ , $b=-8$ and $c=14$ .

The discriminant is $b^2-4ac = (-8)^2-4*1*14 = 64 - 56 = 8$ .

Since this is positive, the quadratic has 2 distinct real solutions.

Note that since the discriminant is not a square number, the solutions are not rational, let alone integers.

How do you find the discriminant and how many solutions does m^2-8m=-14m^2-8m=-14 have?