Posted by Test on .
âˆš(5x4) = 7  âˆš(13x)
before we do anything, remember we cannot take the square root of a negative so,
5x4â‰¥0 and 13xâ‰¥0
xâ‰¥4/5 and x â‰¤ 13
now back to the question,
square both sides
5x4 = 49  14âˆš(13x) + 13x
14âˆš(13x) = 66  6x
7âˆš(13x) = 33  3x
square it again:
49(13x) = 1089  198x + 9x^2
9x^2149x + 452 = 0
x = (149 ± âˆš5929)/18
= (149 ± 77)/18
x = 95 or 4
We can rule out the x=95 since it falls outside our domain established above
So let's test x=4, (answers must be verified after a squaring process)
if x = 4
LS = âˆš(204) = âˆš16 = 4
RS = 7  âˆš9 = 73 = 4
x = 4

Check on Test : Test 
Reiny,
This looks like the reply I tried to send yesterday and wouldn't work.
My square roots signs, which didn't come our correctly are done on my Mac by using " Option V "
This has worked for me for years.
Here is the original reply I tried posting
√(5x4) = 7  √(13x)
before we do anything, remember we cannot take the square root of a negative so,
5x4≥0 and 13x≥0
x≥4/5 and x ≤ 13
now back to the question,
square both sides
5x4 = 49  14√(13x) + 13x
14√(13x) = 66  6x
7√(13x) = 33  3x
square it again:
49(13x) = 1089  198x + 9x^2
9x^2149x + 452 = 0
x = (149 ± √5929)/18
= (149 ± 77)/18
x = 95 or 4
We can rule out the x=95 since it falls outside our domain established above
So let's test x=4, (answers must be verified after a squaring process)
if x = 4
LS = √(204) = √16 = 4
RS = 7  √9 = 73 = 4
x = 4