Basic and advanced example

1. Solving Radical
Equations
By Richard Demolina

2. Steps:
1) Isolate the radical
2) Square both sides of equation
3) Solve for 𝑥
4) Check for extraneous
solutions!

3. Example (basic):
Solve: 2𝑥 + 1 − 1 = 2
1) Isolate the radical :
2𝑥 + 1 − 1 + 1 = 2 + 1
2𝑥 + 1 = 3
2) Square both sides of equation
3) Solve for 𝑥
4) Check for extraneous solutions!

4. Example (basic):
Solve: 2𝑥 + 1 − 1 = 2
2) Square both sides of equation
2𝑥 + 1
2
= 32
2𝑥 + 1 = 9
3) Solve for 𝑥
4) Check for extraneous solutions!

5. Example (basic):
Solve: 2𝑥 + 1 − 1 = 2
3) Solve for 𝑥
2𝑥 + 1 − 1 = 9 − 1
2𝑥
2
=
8
2
𝑥 = 4
4) Check for extraneous solutions!

6. Example (basic):
Solve: 2𝑥 + 1 − 1 = 2
4) Check for extraneous solutions!
2𝑥 + 1 − 1 = 2
2(4) + 1 − 1 = 2
8 + 1 − 1 = 2
9 − 1 = 2 Answer checks!

7. Example (advanced):
Solve: 𝑥 − 4 = 4 − 𝑥
1) Isolate the radical :
No need to here since the radical is already
isolated.
2) Square both sides of equation
3) Solve for 𝑥
4) Check for extraneous solutions!

8. Example (basic):
Solve: 𝑥 − 4 = 4 − 𝑥
2) Square both sides of equation
𝑥 − 4
2
= 4 − 𝑥 2
𝑥 − 4 = 16 − 8𝑥 + 𝑥2
3) Solve for 𝑥
4) Check for extraneous solutions!

9. Example (basic):
Solve: 𝑥 − 4 = 4 − 𝑥
3) Solve for 𝑥
𝑥 − 4 = 16 − 8𝑥 + 𝑥2
0 = 20 − 9𝑥 + 𝑥2
0 = 𝑥 − 4 ( 𝑥 − 5 )
𝑥 = 4 , 𝑥 = 5
4) Check for extraneous solutions!

10. Example (basic):
Solve: 𝑥 − 4 = 4 − 𝑥
4) Check for extraneous solutions!
4 − 4 = 4 − 4 = 0 checks!
5 − 4 = 4 − 5 → 1 ≠ −1 Does not check
therefore extraneous!
Final Solution x = 4