# Evaluating an expression based on a given expresson

If $x^2 + 4x = 10$, evaluate the expression $E = (x + 3)^2 + (x+1)^2$

I don't know what these type of problems are called, hence the odd title and tags. I'd like somebody to tell me what sort of problem this is (what it's called) so I can do self-research or give me some sort of hint to point me in the direction of solving it.

• I would just call this "polynomial algebra", or something like that. In this case, you can expand to get $E[x]=x^2+6x+9+x^2+2x+1=2x^2+8x+10$ and at this point you can use the equation that $x$ is known to satisy.
– lulu
Sep 8, 2015 at 23:30
• I see, but why is there a "[x]" in front of the E in "E[x]=x2+6x+9+x2+2x+1=2x2+8x+10?"
– Ben
Sep 8, 2015 at 23:32
• In my expression? I just meant to indicate that $E$ was a function of $x$. Probably should have omitted it.
– lulu
Sep 8, 2015 at 23:33

For your particular question, you only need the $(a+b)^2=a^2+2ab+b^2$ formula and the basic grouping rules. By using it, you get:
E=$x^2+6x+9+x^2+2x+1=2x^2+8x+10=2(x^2+4x)+10=2 \cdot 10 +10=30$