Karen has been working on her math homework for a very long time. Dakota asked about the methods Karen was using to solve each equation.

Part I: Evaluate
Take a look at Karen's work and then show her a more efficient way of finding each solution.

Karen’s Work
Better Method for Solving
Problem #1:
2x2 = 200

Method Selected: Quadratic Formula
Karen’s Work:

Problem #1:
2x2 = 200

Method Selected:
Your Work:

Problem #2:
x2 – 4x – 5 = 0

Method Selected: Completing the Square
Karen’s Work:

x2 – 4x – 5 = 0

x2 – 4x = 5

x2 – 4x + 4 = 5 + 4

(x – 2)2 = 9

x – 2 = ± 3

x = 2 + 3 and x = 2 – 3

x = 5 and x = –1

{–1, 5}
Problem #2:
x2 – 4x – 5 = 0

Method Selected:
Your Work:

Problem #3:
x2 – 144 = 0

Method Selected: Quadratic Formula
Karen’s Work:

x2 – 144 = 0

x = 12 and x = –12

{–12, 12}
Problem #3:
x2 – 144 = 0

Method Selected:
Your Work:

Problem #4:
(x – 4)2 = 25

Method Selected: Quadratic Formula
Karen’s Work:

(x – 4)2 = 25

x2 – 8x + 16 = 25

x2 – 8x + 16 – 25 = 25 – 25

x2 – 8x – 9 = 0

{–1, 9}
Problem #4:
(x – 4)2 = 25

Method Selected:
Your Work:

Problem #5:
x2 – 16x + 64 = 0

Method Selected: Completing the Square
Karen’s Work:

x2 – 16x + 64 = 0

x2 – 16x = –64

x2 – 16x + 64 = –64 + 64

(x – 8)2 = 0

x – 8 = 0

x = 8

{8}
Problem #5:
x2 – 16x + 64 = 0

Method Selected:
Your Work:

Part II: Compare and contrast
Choose two of the equations to compare and contrast problem solving strategies and solutions. Did Karen get the correct answers? Why do you think it took her over two hours? (Note: Use at least two of this module’s vocabulary words in your response.)

PLZ help 35 points