1. I can solve radical equations and identify extraneous solutions
Warm Up
Simplify: 3− (−1) 2
Solve: 2𝑥 4 +3= 9−𝑥 4
Solve: 3 𝑥 2 +7𝑥−20=0
Solve for m: 4𝑟−3𝑚<6𝑚−10𝑟+27
Multiply: (𝑥−6) 2
Learning Goal
I can solve radical equations and identify extraneous solutions

2. Warm Up
Simplify: 3− (−1) 2

3. Warm Up
Solve: 𝑥 4 +3= 9−𝑥 4

4. Warm Up
Solve: 3 𝑥 2 +7𝑥−20=0

5. Warm Up
Solve for m: 4𝑟−3𝑚<6𝑚−10𝑟+27

6. Warm Up
Multiply: (𝑥−6) 2

7. Solving Equations with Radicals
Working in your table groups, try to solve the following equations:
𝑥 =10
𝑥 −1=8
3 2𝑥−4 =−3
3 𝑥+4 =−1
2𝑥+20 =𝑥
You might need this:
𝑥= −𝑏± 𝑏 2 −4𝑎𝑐 2𝑎

8. 𝑥 =10
𝑥 −1=8
3 2𝑥−4 =−3
3 𝑥+4 =−1

9. 2𝑥+20 =𝑥

10. Summary: Solving Equations with Radicals

11. Practice 3𝑏+25 =2 −4= 4𝑥+8 −10 −7 50−𝑚 =−49 𝑏−9 = 2𝑏−22 −4+5𝑥 =𝑥
Proficient
Advanced
3𝑏+25 =2
−4= 4𝑥+8 −10
−7 50−𝑚 =−49
𝑏−9 = 2𝑏−22
−4+5𝑥 =𝑥
−7 50−𝑚 +4=−45
11=−3+2 𝑚+7
𝑛= −30+13𝑛
𝑚+2= 4𝑚+68

12. Practice 𝑏=−7 𝑥=7 𝑚=1 𝑏=13 𝑥=1 and 𝑥=4 𝑚=1 𝑚=42 𝑛=10 and 𝑛=3 𝑚=8
Proficient
Advanced
𝑏=−7
𝑥=7
𝑚=1
𝑏=13
𝑥=1 and 𝑥=4
𝑚=1
𝑚=42
𝑛=10 and 𝑛=3
𝑚=8

13. Extraneous Solutions 𝑥= 2𝑥+3 𝑥 2 =2𝑥+3 𝑥 2 −2𝑥−3=0 𝑥−3 𝑥+1 =0 𝑥=3 𝑥=−1
Solve the system algebraically 𝑦= 2𝑥+3 𝑦=𝑥
𝑥= 2𝑥+3
𝑥 2 =2𝑥+3
𝑥 2 −2𝑥−3=0
𝑥−3 𝑥+1 =0
𝑥=3 𝑥=−1

14. Extraneous Solutions
Solve the system graphically 𝑦= 2𝑥+3 𝑦=𝑥

15. Extraneous Solutions
When we solve the system algebraically 𝑦= 2𝑥+3 𝑦=𝑥 𝑥=−1 If we plug our solution 𝑥=−1 into the bottom equation: 𝑦=−1 But if we plug our solution into the top equation: 𝑦= 2 −1 +3 𝑦= 1 𝑦=1 1≠−1
𝑥=3
The answer should be only the positive root

16. BUT the original equation was 𝑥= 2𝑥+3
Extraneous Solutions
When a result from a solution process does not make both equations true, it is called an extraneous solution
WHY??
𝑥 2 −2𝑥−3=0
𝑥 2 =2𝑥+3
𝑥= 2𝑥 or 𝑥=− 2𝑥+3
BUT the original equation was 𝑥= 2𝑥+3
When an equation starts with a radical, plug your solution(s) back in to check for extraneous solutions

17. Extraneous Solutions
Solve the system. Be sure to check your answer for extraneous solutions. 𝑦=𝑥−2 𝑦= −3𝑥+16 𝑥=4

18. Homework
Page 223 Problem 5-7
Page 226 Problem 5-20a
Page 230 Problem 5-38