Question

Can someone help me find the solutions of g(x).?
g(x) = x2 +6x + 1
I have no idea how to do this... i need to show step by step on how...

Answer 1

Is g(x) the same as f(x)? Or is it something completely different?

Answer 2

i honestly have no clue...

Answer 3

You can't factorize it, so you can complete the square?

Answer 4

thats what i need to do. but i have no idea how

Answer 5

im in algebra 2 for FlVS.

Answer 6

\[(x+3)^2 - 9 +1\]

Which gives you

\[(x+3)^2 - 8 \]

So you take your number on x, so 6 in this case and half it to give you what goes into the bracket

Answer 7

and if you don't know how to complete the square, you can use the quadratic formula.

\(\scriptsize\color{ slate }{\scriptsize{\bbox[5pt, royalblue ,border:2px solid royalblue ]{~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ }}}\)

quadratic formula.
\(\normalsize\color{ slate }{\Huge{\bbox[5pt, lightcyan ,border:2px solid black ]{ \LARGE{x=~} \huge{ \frac{-\color{magenta}{b} \pm\sqrt{ \color{magenta}{b} ^2-4 \color{blue}{a} \color{red}{c}}}{2 \color{blue}{a}} }~ }}}\)

when the equation is \(\LARGE\color{black}{ \color{blue}{a} x^2+ \color{magenta}{b}x+ \color{red}{c}=0 }\)

Answer 8

Then, you use the square of whatever number is inside the bracket, so 3, and take this away from the overall equation, in relation to any additional terms

Answer 9

Or you could do as SolomonZelman says and use the quadratic formula

Answer 10

im trying to figure this out with what @Green101 said, and i dont really know how to use that formula @SolomonZelman put..

Answer 11

So do you get the rough idea of what I'm talking about?

Answer 12

i just tried to do it and i think i did it right.

Answer 13

Want to show me?

Answer 14

x^2+6x+1=0
x^2+6x=-1
(x+3)^2=-1+8
(x+3)^2=8x
x+3=±SQRT(8)
x=-3±SQRT(8)

Is this right.?

Answer 15

whoops lemme change that.

Answer 16

x^2+6x+1=0
x^2+6x=-1
(x+3)^2=-1+8
(x+3)^2=8x
x+3=SQRT(8)
x=-3+SQRT(8)

Answer 17

You can obtain your solutions from the completed square form :)

So, I can show you how to do it again if you like?

Answer 18

please do.

Answer 19

Ok

\[g(x) = x^2+6x+1\]

Answer 20

So to complete the square you do

\[(x+3)^2 - 9\] which when expanded gives you \[x^2 + 6 \] but since you want to expand to give your original equation you have to add 1

Answer 21

so what would the solution be.?

Answer 22

so your completed square form is
\[(x+3)^2-8\]

Answer 23

ok so this is what im turning in as the answer,

x^2+6x+1=0
x^2+6x=-1
(x+3)^2=-1+8
(x+3)^2=8x
x+3=±SQRT(8)
x=-3±SQRT(8)
Completed is (x+3)^2-8

Answer 24

x^2+6x+1=0
x^2+6x=-1
(x+3)^2=-1+8
(x+3)^2=8x
x+3=SQRT(8)
x=-3+SQRT(8)
Completed is (x+3)^2-8

Answer 25

Not quite, from (x+3)^2 - 8 I would say that your solutions are -3 and -8. But I would bump this question to make sure :)

Answer 26

oh one more thing @Green101

would "We start by completing the square with the x^2 and x term. We have to subtract the ^2 of the constant, and multiply by the value if the factored number (-16). And then we simplyfy the extra numbers that arent a part of the factored number." be correct if i was explaining how to convert f(x) into the general, vertex form of the equation

Answer 27

That I can't help with sorry, I've never ever been asked that at college XD

Answer 28

Like I say bump the question and people will help!

Answer 29

im in 10th grade math Cx

Answer 30

and okayy thanks for the help :)