Help with radical equations pleaseee? ten points!!!

I am so desperate. I have 33 assignments to do before tomorrow.
Please help me finish this one up. I don't even know how to start this.:c

1. √8x+1 = 5

3. -4√x+9=20

4. √6x+5=√53

5. √x+2 +4 = x

Isolate the radical expression first, then square both sides. You should check all possible solutions in the original equation, because squaring both sides sometimes gives apparent solutions.
1. √8x+1 = 5 It’s not clear to me if x is under the radical sign or not. I’ll show solutions for both.
If x is not under the radical sign:
√8x+1 = 5
√8x = 4
(√8x)^2 = 4^2
8x^2 = 16
x^2 = 2
√(x^2) = ±√2
x = ±√2
Check x = √2
√8(√2)+1 = 5
√16 + 1 = 5
4 + 1 = 5
5 = 5 checks
Check x = - √2
√8(-√2)+1 = 5
-√16 + 1 = 5
-4 + 1 = 5
-3 = 5 does not check
Solution: x = √2

If x is under the radical sign:
√(8x)+1 = 5
√(8x) = 4
(√(8x))^2 = 4^2
8x = 16
x = 2
Check:
√(8*2)+1 = 5
√16+1 = 5
4 + 1 = 5
5 = 5 checks
Solution: x = 2

3. -4√x+9=20
-4√x= 11
√x = -11/4
(√x)^2 = (-11/4)^2
x = 121/16

Check:
-4√(121/16) + 9 = 20
-4(11/4) + 9 = 20
-11 + 9 = 20
-2 = 20 does not check
No solution
Notice you could have determined that there is no solution on the third step in the solution √x = -11/4.
√x refers to the principle square root, which is a positive number, so it can’t equal a negative 11/4.





4. I’m assuming you meant √(6x+5)=√53
When an equation has two radical expressions, make sure you separate the radicals, one on each side of the equation. In this problem, the radicals are already separated Now square both sides.
(√(6x+5))^2=(√53)^2
6x + 5 = 53
6x = 48
x = 8
Check:
√(6*8+5)=√53
√(53)=√53 checks
Solution: x = 8


5. I’m assuming you meant √(x+2) +4 = x
√(x+2) = x – 4 -------> isolate the radical expression on one side
(√(x+2))^2 = (x – 4)^2
x+2 = (x-4)(x-4)
x+2 = x^2 – 8x + 16
x^2 – 9x + 14 = 0
(x – 7)(x – 2) = 0
x=7 or x=2
Check x=7
√(7+2) +4 = 7
√9+4 = 7
3 + 4 = 7
7 = 7 checks
Check x=2
√(2+2) +4 = 2
√4+4 = 2
2 + 4 = 2
6 = 2 does not check
Solution: x = 7