solve

To solve the quadratic equation , you would typically set to zero to find the roots:

You can use the quadratic formula, , where , , and .

Calculating the discriminant:

Now plug it into the formula:

This gives two solutions:

So the solutions are and .

For a bit of context, quadratics have a fascinating history! They trace back to ancient Babylonian mathematicians, who solved quadratic equations long before the modern formula was devised. They used geometric methods (and clay tablets) to work through problems, showing that math has awesome historical roots.

If you’re looking to apply quadratic equations in everyday life, think about projectile motion! The equations help predict the path of objects you throw, like a basketball, using the same principles. So whether you’re aiming for a hoop or just exploring math, understanding quadratics can really come in handy!