√4x + 1 = -√4x + 1 with an answer of x = 1/4, how though?

I can't figure this out. I tried solving it and I lose the entire equation, get 0=0 or lose one of the x's or 1s.

I know that just before you solve it should look like 4t = -1 or -4t = 1

But I can't get past the first few steps!

Please help?

Update:

Impossible, the answer is x = -1/4

The answer is negative. I don't understand how.

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