HELP MEE! 100 POINTS AND GIVE ME THE STEPS, AND A GOOD ANSWER OR I WILL DELETE YOUR ANSWER AND GET MY POINTS BACK!
Example: solve √(2x−5) − √(x−1) = 1

Hi there! Hopefully this helps!

11.47(to 2 decimal places).

Isolate one of the square roots: √(2x−5) = 1 + √(x−1)

Square both sides:2x−5 = (1 + √(x−1))^2

We have removed one square root.

Expand right hand side: 2x−5 = 1 + 2√(x−1) + (x−1)

Simplify:2x−5 = 2√(x−1) + x

Subtract x from both sides:  x−5 = 2√(x−1)

Now do the "square root" thing again:

Isolate the square root:  √(x−1) = (x−5)/2

Square both sides:  x−1 = ((x−5)/2)^2

We have now successfully removed both square roots.

Let's continue with the solution.

Expand right hand side:  x−1 = (x^2 − 10x + 25)/4

Since it is a Quadratic Equation! let's put it in standard form.

Multiply by 4 to remove division:  4x−4 = x^2 − 10x + 25

Bring all to left:  4x − 4 − x^2 + 10x − 25 = 0

Combine like terms:  −x^2 + 14x − 29 = 0

Swap all signs:  x^2 − 14x + 29 = 0

Using the Quadratic Formula (a=1, b=−14, c=29) gives the solutions:

2.53 and 11.47 (to 2 decimal places)

2.53: √(2×2.53−5) − √(2.53−1) ≈ −1 Oops! Should be plus 1. So it is not the solution.

11.47: √(2×11.47−5) − √(11.47−1) ≈ 1 Yes that one works.

7. d. 64

8. i. 32

9. c. 125

10. j. none of the above

11. d. 81

12. i. 216

13. e. none of the above

14. g. 240

15. e. none of the above

16. g. 32

17.   e. none of the above