I am a math tutor looking for a better way to explain quadratics to my students.
I came across the so-called "Po-shen Loh" method on YouTube, and I tried to apply it to a quadratic equation that one of my students was having trouble with. (Here is the video that I learned it from, skipped to the example that is most similar to my problem: https://youtu.be/XKBX0r3J-9Y?t=1663)
The equation that I want to solve is $5x^2 – 4x – 6 = 0$
Here is the correct result, as confirmed by symbolab (https://www.symbolab.com/solver/quadratic-equation-calculator/solve%20for%20x%2C%205x%5E%7B2%20%7D-4x-6%3D0):
$$
x_{1,2} = \frac{2 \pm \sqrt{34}}{5}
$$
However, when I try to work it out using the "Po-shen Loh" method, I keep getting this result:
$$
x_{1,2} = \frac{2 \pm \sqrt{40}}{5}
$$
Here are my calculation steps, please help me if you can:
Best Answer
(I am eternally grateful to player3236)
My mistake was in the line:
$\frac{2}{5} - u^2=-\frac{6}{5}$
However, this should have been:
$\frac{4}{25} - u^2=-\frac{6}{5}$
Why? In the immortal words of player3236:
$(2/5 - u)(2/5 + u) \neq 2/5 - u^2$
The "Poh-shen Loh" method involves a difference of squares at that stage in the calculation.