Determine the number and type of solutions of the given quadratic equation. Do not solve. x 2 + 8 x + 16 = 0 x^2+8x+16=0 x 2 + 8 x + 16 = 0

Hey, everyone. In this problem, we're asked to determine the number and type of solutions this quadratic equation has without solving, which we can do by using the discriminate. So here I have x squared plus 8x plus 16 is equal to 0. And remember, my discriminant is given by b squared minus 4ac. So let's go ahead and calculate that. Now our a value is just this 1, b is positive 8, and c is positive 16. Let's go ahead and plug that all in. So b is going to be 8 squared minus 4 times a, which is 1, times c, which is 16. Now 8 squared, we know is 64 minus 4 times 1 is just 4, and 4 times 16 is also 64. So I end up with 64 minus 64, which gives me 0. Now remember when our discriminate is 0, that tells us that we're going to have one real solution to our quadratic equation, and this is our final answer here. We have one real solution, and we didn't have to solve our quadratic equation. Let me know if you have questions.