SOLUTION: sqrt(x^2-2)/sqrt(7 x-25)= sqrt(2) I need help its me for Find all real solutions of the equation. (If there are extra answer boxes, enter NONE in the last boxes.) ive tried every

Question 321244: sqrt(x^2-2)/sqrt(7 x-25)= sqrt(2)
I need help its me for Find all real solutions of the equation. (If there are extra answer boxes, enter NONE in the last boxes.) ive tried everything but i still do not understand can you send me how you guys performed this operation i'd appreciate it thanks
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
=
this can be written under a single radical on the left
=
Now we have a single radical on each side, square both sides and we're rid of em
= 2
Multiply both sides by (7x-25), and you have
:
x^2 - 2 = 2(7x - 25)
:
x^2 - 2 = 14x - 50
arrange as a quadratic equation on the left
x^2 - 14x - 2 + 50 = 0
:
x^2 - 14x + 48 = 0
Easily factors to
(x-8)(x-6) = 0
Two solutions
x = 8
and
x = 6
:
Check both these solutions in the original problem using a calc
x=8
=
= 1.414
= 1.414; confirms this solution
:
You should check x=6, the same way
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