c) Isolate the \( x \) on the left by moving the other term to the right d) Write the right-hand side as a single fraction If you have followed the steps correctly you have established quadraic formala, ie. for a quadratic equation of the form \( a x^{2}+b x+c=0 \), solutions are: \( 2.7 x= \)

The quadratic formula has quite an interesting historical background! It dates back to ancient Babylonians who solved quadratic equations as early as 2000 BCE, using geometric methods. However, the formula we commonly see today, \( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \), was formalized much later in the Middle Ages by mathematicians across the globe, including Arab scholars and Europeans like René Descartes. Now, let’s talk about a real-world application. Quadratic equations can help solve various real-life problems, such as predicting the trajectory of a projectile or optimizing areas. For example, if you throw a ball, its height can be modeled by a quadratic equation, allowing you to determine the time it will take to hit the ground again or find the maximum height it reaches. Mathematics in motion, quite literally!