Question

Find the range of values of x for (x-3)^2 < or equal 14 - 2x

Answer 1

\[x \in [-1,5]\]

Answer 2

\[(x - 3)^2 \le 14 - 2x\]
\[(x -3)^2 -14 +2x \le 0\]
\[\text{Let } f(x) = (x -3)^2 -14 +2x\]
\[f(x) \le 0 \]
\[(x -3)^2 -14 +2x \le 0 \implies x^2 + 9 - 6x + 2x -14 \le 0 \implies x^2 - 4x - 5 \le 0 \]
\[\implies x^2 - 5x + x - 5 \le 0 \implies x(x -5) + 1(x -5) \le 0 \implies (x - 5)(x +1)\le 0 \]
\( ++++\) \( ---- \) \( ++++\)
<-----------------------------|-------------------------|------------------------------------------------->
\(-\infty\) -1 5 \(\infty\)



Hence, \(x \in [-1,5]\) is the Solution.

Answer 3

That's Cheating :-p lol

Answer 4

why?

Answer 5

I was kidding

Answer 6

i answered almost 10 minutes before u :P

Answer 7

sorry, 4 minutes..

Answer 8

3 and a Half :-P but I have the solution too

Answer 9

great :D

Answer 10

nobody's giving me a medal :(

Answer 11

You Just Got one! :-D