The original equation was

1.7e-3 = (0.0015 -x)^2 / (0.025 +1/2x)(0.025 + 1/2x)

Square root of both sides is
0.0412 = (0.0015-x) / (0.025 + 1/2x)

Solve for x and when I put in -0.001 or 1.0e-3 it says that it is incorrect, I don't know why??

I don't know what the left side of your equation is

is it 1.7e^-3 ?
then its square root would be .290926
is it 7e^-3, with the beginning saying it is question #1 ?
then its square root would be .59035

please clarify

Also to have the result to be your stated right side, the original right side would have to be

(0.0015 -x)^2 /( (0.025 +1/2x)(0.025 + 1/2x) )

how did you get x=0.001 or -0.001?

Is the question
1.7e-3 = [(0.0015 -x)^2 / (0.025 +1/2x)](0.025 + 1/2x)
or
1.7e-3 = (0.0015 -x)^2 /[(0.025 +1/2x)(0.025 + 1/2x)]
They are completely different equations if parentheses are omitted.
Remember that to transcribe a fraction from a book, you need a set of parentheses around the numerator and another set around the denominator.

The equation is written as

1.7e-3 = (0.0015-x)^2 / (0.025 + 1/2x)(0.025 + 1/2x)

in that case 1.7e^-3 = .0846..

and after you take the square root , you get .2909...

As pointed out by MathMate and posted my me above,
you still did not correct your denominator.
The way you typed it, the .025 + 1/2x would cancel out.

Does e^(-3) mean 2.7182818284....^(-3), or does it mean 10^(-3) as is used in computer representation?

It begins to appear that 1.7e-3 is 1.7E-3, using scientific notation. All bets are off above.

yes , it is 10^(-3). I sorry,im just so confused. I am typing it exactly as it is shown on my homework. They used().