Q. Solve using the quadratic formula.

What are , and ?

What is the discriminant?
After using the quadratic formula, what are the values of ?

Alright, let’s dive into the quadratic equation (after moving all terms to one side).

First, you identify the coefficients: , , and .

Now, for the discriminant, we calculate it using , which gives us . So, the discriminant is , and that means we will have two real and distinct solutions!

Using the quadratic formula , we find the values of :

So the final solutions are and .

Now let’s spice things up with a bit of fun knowledge!

Did you know that quadratic equations have been studied for over 2000 years? Ancient Babylonian mathematicians were already solving quadratic equations well before the term was even coined! They had methods that were surprisingly close to our modern techniques, showing that even back then, humans had a curiosity for numbers.

And speaking of quadratics, they pop up everywhere! From the trajectory of a basketball to the design of a parabolic satellite dish, understanding how they work is not just about passing tests. It’s like having a superhero tool for tackling real-world problems - truly illuminating how math shapes our world!