We start with this:
[tex] \sqrt{[tex] 2x^{2} [/tex]-7} [/tex]-1=4
Add 1 to both sides to get:
[tex] \sqrt{ 2x^{2}-7} [/tex]=5
Now, to get rid of that nasty square root, we square both sides:
[tex] (\sqrt{2x^{2}-7}) ^{2} [/tex] = [tex]5^{2} [/tex]
You're left with this:
[tex] 2x^{2} -7[/tex] = 25
Add 7 to both sides to get:
[tex] 2x^{2} [/tex] = 32
Now square root both sides to get rid of the square on 2x:
[tex] \sqrt{2x^{2} } [/tex] = [tex] \sqrt{32} [/tex]
Since 32 isn't a perfect square we're gonna leave it as a square root.
Now divide both sides by 2 and get your answer:
x = [tex] \frac{\sqrt{32}} {2} [/tex]
