Question

7x+2= x√5
Can anyone walk me through this please

Answer 1

First, you need to gather all the terms containing x on one side of the equation. Can you do that?

Answer 2

yeah

Answer 3

Go ahead. What do you have?

Answer 4

so 7x-x√5 = -2

Answer 5

Terrific. Now, x is a common factor on the left hand side. Can you factor out the x?

Answer 6

yeah
x(7-√5) =-2

Answer 7

Great. Now, to solve for x, divide both sides by \(7-\sqrt{5}\)

Answer 8

ok so it becomes x = -2/7-√5 and thats it?

Answer 9

Well not quite. Depends on what your teacher expects. Most times we don't want to leave a square root (irrational number) in the denominator, so we would rationalize the denominator. Do you know what I'm talking about?

Answer 10

oh yeah you have to multiply by conjugate

Answer 11

i just remembered

Answer 12

Exactly. Multiply your answer by the conjugate over the conjugate.

Answer 13

so it becomes -1/27

Answer 14

right?

Answer 15

Don't think so. Let me detail it a bit...

Answer 16

ok

Answer 17

\[x=\frac{ -2 }{ 7-\sqrt{5} }\times \frac{ 7+\sqrt{5} }{7+\sqrt{5} }\]Can you complete this?

Answer 18

Oh i forget to multiply the top i did it in my head

Answer 19

\[-14+2√5 / 49 +5\]

Answer 20

Close. Check the signs in the numerator. And the denominator is going to be 49-5

Answer 21

yeah is se

Answer 22

see*

Answer 23

So the final answer is\[−7+1√5/22\]

Answer 24

i simplified

Answer 25

Excellent. And you don't need to write the 1 before the square root sign.

Answer 26

But hold on i have the same exact answer on my test and I got it wrong i put a plus or minus but my teacher took off a ll the points he usually takes of like half

Answer 27

and h crossed out my entire process

Answer 28

i squared both sides when i started solving is that why?

Answer 29

can i not do that

Answer 30

Can't help you there. You'll have to ask your teacher about that. But the work you've done here is correct.

Answer 31

Ok no problem thank you so much for the help

Answer 32

You wouldn't solve this problem by squaring. IN this case, you can't get rid of the square root by squaring both sides.

Answer 33

You're welcome