Solve Analytically. See comments

Question

jpes2193 · Answer

$$\sqrt{4x+13}+1=2x$$

jpes2193 · Answer

a small step by step would be appreciated.

dtan5457 · Answer

Was afk, sorry.

Anyways, a step by step it is.

1. Subtract the 1 to the other side

$$\sqrt{4x+13}=2x-1$$
Square both sides to get rid of the radical
$$4x+13=4x^2-4x+1$$
Get like terms on one side
$$4x^2-8x-12=0$$
Factor, quadratic formula, whatever works for you.

dtan5457 · Answer

Once you factor it, check for extraneous solutions (because there is one)

jpes2193 · Answer

you know i really just need to go with my gut on starting these problems..

dtan5457 · Answer

Haha, you got it now?

jpes2193 · Answer

yea checking for extraneous would be plugging the answers back into the original equation right

dtan5457 · Answer

Yep, an extraneous solution would not make the equation true

jpes2193 · Answer

okay let me plug away at this an see what I get

dtan5457 · Answer

Any luck?

jpes2193 · Answer

I got -1,3 and both make the equation =0

dtan5457 · Answer

Hmm, want to show some work so I can find a mistake?

jpes2193 · Answer

give me a sec and I'll have it up.

dtan5457 · Answer

No problem, take your time. Props to you for trying on each problem.

jpes2193 · Answer

WAIT?!?! wouldn't 4 be the extraneous solution because 4 does not = 0

dtan5457 · Answer

Oh wait a minute, I think I see your problem.

dtan5457 · Answer

You don't plug -1,3 into the quadratic, but into the original equation.

dtan5457 · Answer

If you plug it into the quadratic, both are gonna look true since you factored it directly from the quadratic.

Plug -1,3 into the original question

jpes2193 · Answer

light bulb.

dtan5457 · Answer

Lol, which one is extraneous. ?

jpes2193 · Answer

-1

dtan5457 · Answer

bingo

dtan5457 · Answer

your answer is 3 :)

jpes2193 · Answer

Thank you :)

dtan5457 · Answer

yw