You are welcome. You will find several methods in that book,

]]>Welcome to the forum.

There are Descartes' and Ferrari's solutions for the general quartic but they are both difficult. There are no algebraic solutions for the general quintic or higher.

Download "First Course in the the Theory of Equations." It is free!

http://www.gutenberg.org/ebooks/29785

Down the page are the links.

Starting at page 56 of that book you will find everything you need.

If you need help with the examples he provides just post here.

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Later on, I drew a set of scales to visualise the fact that I needed to do the same to each side.

Then I did the same method, but without the drawing, just lots of lines of working.

And now I'm able to do all kinds of crazy algebra in my head.

Just take small steps at a time.

Thereafter, the lessons were on simple operations of addition, division, multpilication, subtraction, extracting roots, exponentiation etc.

The next step was solving linear equations in one variable, simultaneous equations of two, three variables. A little later I learnt solving quadratic equations and their properties. I forgot to mention, I was also taught plotting graphs and solving equations with graphs.

The Binomial theorem was the last I was taught, and Pascal's triangle too.]]>

2 + ? = 6

What does the "?" equal?

Then I go on to say that it is better to put an "x" instead:

2 + x = 6

What does the "x" equal?

start with obvious things

x=x

x+x=x+x

2x=x+x

2x+x=x+x+x

3x+x=x+x+x+x

now

a(z+z')=az+az'

b(a(z+z')=(ab)(z+z')=abz+abz'

I'm not a teacher, but if I were, I would shurelly avoid fruit-algebra in my classes.

]]>Plus, I have a very useful ability to understand things quickly.

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