Question

how do I solve this: 3x+sqrt(x-1)=x+2

Answer 1

I need to solve for x, then check the answer
I tried the quadratic equation but it got super complicated and was wondering if anyone knew a good way to solve this

Answer 2

here's my work at the moment...
sqrt(x-1)=-2x+2

x-1=4x^2+4

x-5=4x^2

-4x^2+x-5=0

-1+/- sqrt(1-80) /-8

(-1+/-sqrt(-79))/-8

-1/8(-1+i sqrt(79) -1/8(7.9i)=-.9875i

-1/8(-1-i sqrt(79) -1/8(-9.9i)=1.2375i

3(-.9875i)+sqrt(-.9875i-1)=-.9875i+2

Answer 3

you've gone wrong in the second line
(-2x + 2)^2 = 4x^2 - 8x + 4

Answer 4

Thx... was it right to do the quadratic formula, or was there an easier equation to try?

Answer 5

so x-1 = 4x^2 - 8x + 4
4x^2 - 9x + 5 = 0

Answer 6

- you can factor this one

Answer 7

Oh I see can you stay for a bit I might need some help still

Answer 8

Thank you very much

Answer 9

(x-1)(4x-5)?

Answer 10

yes

Answer 11

sorry I'm in algebra 2 and I only learned how to factor and put into the standard form. Can you just tell me the gist on solving for x from here? Sorry

Answer 12

ok if ab = 0 then either a and b must be 0
here (x-1)=0 or (4x-5)=0

Answer 13

* thats a or b

Answer 14

Ok so the answer is either 1 or 5/4, just need to check one fits into the orginal problem?

Answer 15

right - one of these roots might be extraneous

Answer 16

Thank you very much.

Answer 17

yw