Question
Solve the equation for all real solutions in simplest form.

Answer Altempt tout of 2
© Additional Solution © No Solution

To solve the quadratic equation , we can use the quadratic formula . Here, , , and . Plugging in the values, we find the discriminant . Since the discriminant is positive, there are two real solutions.

Now, substituting back into the formula gives us:

So the solutions simplify to and .

The quadratic formula is not just any formula — it’s like a magic key for unlocking the doors of polynomial mysteries! Many students overlook this golden ticket in favor of simpler methods, but it works wonders for any quadratic. Understanding how to apply it not only gives you the answers you seek but also sharpens your algebra skills for future equations.

Practical applications of quadratic equations are everywhere, from optimizing profit in business to determining the trajectory of a flying baseball. In engineering, for instance, quadratic equations pop up in designs that require stability calculations or in the construction of structures, where calculations often need to account for the effects of gravity and angles. So, the next time you swing a bat or shape a building, know that quadratics are there, crunching the numbers behind the scenes!