Question 81517

well it looks sort of like the right steps,
but your algebra is losing terms and factors all over the place

I guess you have a confusion about what is done to balance an equation.

Imagine a see-saw.
On each end of the see-saw is a twin.  Art and Bart.  They both weigh 42 pounds.  A = B
Then you can add a 5 pound weight on each end
A + 5 = B + 5
Now there is 47 pounds on each end

Now you make one of the 5 disappear
A + 5 > B
47 > 42

Please notice carefully here that the equation is not balanced any more.
Now it has become an inequality.
47 and 42 are not the same number.
One twin will now go up into the air and the other one will land on his butt.
This is not a very nice joke to do!  But kind of funny to watch!

What you need is:
{{{2x^2 - 3 = 15}}}
Add 3 to each side.  The same thing is done to each side, so the equation stays balanced!
{{{2x^2 -3 + 3 = 15 + 3}}}
{{{2x^2 = 18}}}
Now you divide BOTH sides by 2 to isolate the x^2 and keep the equation balanced
{{{x^2 = 18/2 = 9}}}
Now the square root can be used
{{{x = +3}}} or {{{x = -3}}}

I am not sure what "the square root principle" is.  I have heard +3 called "the principal square root" of 9 and then -3 is the other square root of 9 that is not the principal one.  People often write "principle" when they really mean "principal", even in prestigious publications such as the Georgia Tech alumni magazine, or in their own job titles, but I hope you will be able to work it out.  Principal is a noun or an adjective, and Principle is always a noun I think.