Determine the number and type of solutions of the given quadratic equation. Do not solve. − 4 x 2 + 4 x + 5 = 0 -4x^2+4x+5=0 − 4 x 2 + 4 x + 5 = 0

Hey, everyone. Let's take a look at this practice problem. Here, we wanna determine the number and type of solutions that this quadratic equation has without solving it. And here we have negative 4x squared plus 4x plus 5 is equal to 0. Now the way that we do this without solving is by using the discriminant, which you remember is b squared minus 4ac. So let's go ahead and calculate that. So our a is going to be negative 4, b is positive 4, and c is 5. Plugging all of that in, b squared is going to be 4 squared minus 4 times a which is negative 4 times c which is 5. Now 4 squared is just 16 and then that's subtracting 4 times negative 4 is going to give me negative 16 and this is multiplied by 5. So further simplifying that, 16 minuteus negative 16 times 5, if I plug that in my calculator, is going to give me negative 80. So final simplification here is going to be 16 +80 because I have that double negative and that's going to give me a 96. Now 96 is a positive number, and whenever I have a positive discriminant, that tells me that I'm going to end up with 2 real solutions. So this is going to be my answer to this question here. And I know that if I were to fully solve this quadratic equation, I would end up with 2 real solutions. Thanks for watching and I'll see you in the next one.