Example:

 

x = √3x+7-1

 

x+1 = √3x+7

 

(x+1)² = (√3x+7)²

 

x²+2x+1 = 3x+7

 

Question: Why +2x?

 

x²-6-x = 0

 

Question: Why -6-x?

 

x = -2 OR x = 3

 

Question: How can you see the answer will be -2 or 3?

At first I thought you had made very strange errors in your working, would I be correct to presume that the very first line is actually this?

 

[math]x = \sqrt{3x+7} - 1[/math]

 

If so the working goes as follows:

 

[math](x + 1)^2 = 3x+7[/math]

 

[math](x + 1)(x+1) = 3x+7[/math]

 

[math]x(x+1) + 1(x+1) = 3x+7[/math]

 

[math]x^2 + x + x+ 1 = 3x+7[/math]

 

[math]x^2 + 2x + 1 = 3x+7[/math]

 

Hopefully that answers your first question.

 

And then we subtract 3x + 7 from both sides:

 

[math]x^2 + 2x + 1 - (3x + 7) = 3x + 7 -(3x + 7)[/math]

 

[math]x^2 - x - 6 = 0[/math]

 

Then factorising:

 

[math](x-3)(x+2) = 0[/math]

 

[math]x-3 = 0[/math] or [math]x+2 = 0[/math]

Thanks for reply. Long story short, it's been many years so I'm taking lower level of math before I jump into this again. Is there a program I can use to make those symbols and print out?

Is there a program I can use to make those symbols and print out?

Here is a Quick LaTeX Tutorial to help you.

Isn't it called "irrational equations"?

 

(I'm a Norwegian too, so I know what "irrasjonelle likninger" is.)