Question

Find the solutions of g(x). Show each step.

g(x) = x^2 +6x + 1

If you could show me how to do this so I can do it in the future, it would be greatly appreciated. (:

Answer 1

\(\large \begin{array}{cccllll}
g(x) = x^2 &+6x &+ 1\\
&\uparrow &\uparrow \\
&3-2&3\cdot -2
\end{array}\)

Answer 2

woops, darn the went wrong =) one sec

Answer 3

I mistook the equation... well
I gather you'd need to use the quadratic formula for this one

Answer 4

since you can't squeeze 6 out of 1

Answer 5

unless you mean \(\bf x^2+1x+6\)

Answer 6

well, not even that one... would work well... unless you meant say \(\bf x^2-1x-6\)

Answer 7

No the equation is g(x)=x^2+6x+1

Answer 8

I'm assuming you're meant to use the perfect square trinomial to solve for "x"?

Answer 9

My instructions just say to find the solutions of g(x). The title of the assignment is completing the square, if that helps..

Answer 10

anyhow...lemme do that instead.... lemme make it a perfect square trinomial

anyhow... to solve quadratics for "x", you'd set y=0, that is g(x) = x^2 +6x + 1 => 0= x^2 +6x + 1 thus \(\bf g(x) = x^2 +6x + 1\implies g(x) = (x^2 +6x+{\color{red}{ 3}}^2) + 1-{\color{red}{ 3}}^2
\\ \quad \\
g(x)=(x+3)^2+1-9\implies g(x)=(x+3)^2-8\quad \textit{setting y=0}
\\ \quad \\
0=(x+3)^2-8\implies 8=(x+3)^2\qquad taking\quad \sqrt{\qquad }
\\ \quad \\
\pm\sqrt{8}=x+3\implies 2\pm\sqrt{2}=x+3\implies 2\pm\sqrt{2}-3=x\)

Answer 11

So the final answer would be 2 plus or minus radical 2 minus 3?

Answer 12

after completing the square and solving for "x", yes
is a QUADRATIC, thus it has 2 answers