Question

sqrt of 3x + 4 minus sqrt of 2x - 7 equals 3

Answer 1

\[\sqrt{3x+4} - \sqrt{2x-7} = 3\]

Answer 2

Could you help me with this problem? :)

Answer 3

Yes. Any ideas how to start? I am a teacher and I will try to drag it out of you rather than just tell you. I won't have you suffer too much though.

Answer 4

use the difference of two squares

Answer 5

I figured you could square both sides first?

Answer 6

Separate the roots first by adding the subtracted one to both sides then let the squaring begin.

Answer 7

so add 2 x + 7

Answer 8

\[\sqrt{3x+4} = 3 + \sqrt{2x-7}\]

Answer 9

So how would I go about getting rid of the 3

Answer 10

You have to square both sides. The right is a binomial being squared. Careful.

(3 + sqrt)(3 + sqrt)

Answer 11

So it would be 3x + 4 = ( 3 + sqrt of 2x - 7 ) ( 3 + sqrt of 2x - 7)?

Answer 12

Yes

Answer 13

Okay so then the next step would be toooo...

Answer 14

FOIL the right side.

Then, believe it or not gather like terms so sqrt is alone and square both sides again.

Answer 15

Okay I offically suck at foiling

Answer 16

3*3 + 3 * sqrt + 3 * sqrt + sqrt ^ 2

Answer 17

So would it be 9 + 3 sqrt of 2x - 7 + sqrt of 2x-7 squared

Answer 18

\[3x +4 =9 + 6\sqrt{2x-7}+2x+7\]

Simplify and isolate the sqrt

Answer 19

So would I add the 3x + 4 and the 2x + 7

Answer 20

Gather terms on the right.

Move anything not sqrt to the left.

What do you get?

Answer 21

sqrt of 2x - 7 + 5 x + 11 = 22 ? that's probably wrong

Answer 22

3x + 4 = 2x + 16 + sqrt

Answer 23

Okay would I square both sides now?

Answer 24

You there

Answer 25

Here

Answer 26

Gather all but 6 sqrt on left side.

Answer 27

So would I add the 3x+4 and 2x+16

Answer 28

(3x+4) - (2x+16) to gather everything to the left

Answer 29

So then it would be 3x + 4 - 2 x + 16 = sqrt of 2x-7 ?

Answer 30

-16 and 6sqrt

Answer 31

What? I'm more visual learner..

Answer 32

Where did you get a 6 from???

Answer 33

Way up where we did foil you see 6 * sqrt.

Answer 34

So how did you get -16 and 6 sqrt

Answer 35

Big picture coming. Hang on.

Answer 36

Alrighty

Answer 37

Any luck??

Answer 38

I am getting there, it's just getting the visual you need takes some time.

Answer 39

I had a sign error. How disgusting!

Answer 40

Oh okay