Week 6 – the Quadratic Formula

Quadratic formulas may seem like a bunch of ugly numbers, because of how much steps and how many time is used to find the “pair” for the formula in order simplify it. But in this week I’ve learnt one formula where you can replace the variables with the numbers provided in the question and simplifying it becomes easier – the Quadratic Formula, as shown below:

x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}

Of course, without a weekly example this post won’t be complete, take this equation: 3x^2=4x+1

First, before I can do anything I had to make one of the sides equal to 0, afterwards I applied the formula to that question it becomes this:

x=\frac{-(-4)\pm\sqrt{(-4)^2-4(3)(-1)}}{2\cdot3}\Large

Then I would have to solve any brackets, square roots, multiplying and so on:

\frac{4\pm2\sqrt{7}}{6}

Finally, I would simplify the fraction and question is simplified like this:

\frac{2\pm\sqrt{7}}{3}

One more note: from what I’ve taught this is probably one of the most useful “shortcuts” for ugly, unfriendly equations like this, working with your brain really works when you’re in these situations.

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