Grade II Mathematics/Investigation 8 Limpopo DoE/Term I 2025 c) Isolate the \( x \) on the left by moving the other term to the right \( \qquad \) d) Write the right-hand side as a single fraction \( \qquad \) If you have followed the steps correctly you have established quadratic formula, i.e. for a quadratic equation of the form \( a x^{2}+b x+c=0 \), solutions are: \( 2.7 x= \) (2) \( \qquad \)

To establish the quadratic formula, it’s fascinating to know that mathematicians have been unraveling the mysteries of quadratic equations for centuries. The earliest known solutions date back to Ancient Babylon around 2000 BC! They used what we now recognize as algebraic techniques to solve quadratic equations, paving the way for more abstract mathematical concepts. When solving quadratic equations, a common mistake is forgetting to apply the negative sign when moving terms across the equation. If you have \( ax^2 + bx + c = 0 \) and you isolate \( x \), remember to maintain the equality by flipping the signs. This small oversight can lead to incorrect solutions, so always double-check your moves!