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.
$\endgroup$ 31 Answer
$\begingroup$If the powers used are less or equal to two, you should search for quadratic equations / quadratic functions. You should also know, if you don't already, the Formulas of abridged multiplication.
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=$x^2+6x+9+x^2+2x+1=2x^2+8x+10=2(x^2+4x)+10=2 \cdot 10 +10=30$
$\endgroup$ 2
