Solve the equation below for x. What is the solution set?

5(x-2)^2=125

Answer : x=-3 or x=7

I know I need to do factoring, just forget how to set it up. I also can't figure out where this -20x+20 came from. Thanks for the assistance.

not much factoring here.

5(x-2)^2 = 125
(x-2)^2 = 25
x-2 = ±5

x-2 = +5: x = 7
x-2 = -5: x = -3

as for the -20x+20,

5(x-2)^2 = 5(x^2-4x+4)
= 5x^2-20x+20

To solve the equation 5(x-2)^2 = 125, you can follow these steps:

Step 1: Divide both sides of the equation by 5 to isolate the squared term:
(x-2)^2 = 25

Step 2: Take the square root of both sides to eliminate the squared term:
√((x-2)^2) = √25

Step 3: Simplify the equation:
x - 2 = ±5

Step 4: Solve for x by adding 2 to both sides of the equation:
x = 2 ± 5

Step 5: Express the solutions in both positive and negative forms:
x = 2 + 5 or x = 2 - 5

Step 6: Simplify the solutions:
x = 7 or x = -3

Therefore, the solution set for the given equation is x = 7 and x = -3.

To solve the equation 5(x-2)^2 = 125, we can start by dividing both sides of the equation by 5 to simplify it:

(x-2)^2 = 25

Now, to eliminate the square, we can take the square root of both sides of the equation:

√((x-2)^2) = √25

This gives us two possibilities:

x - 2 = 5 or x - 2 = -5

Now, let's solve each of these equations separately:

For x - 2 = 5, we can add 2 to both sides of the equation:

x = 5 + 2

Simplifying, we have:

x = 7

For x - 2 = -5, we can add 2 to both sides of the equation:

x = -5 + 2

Simplifying, we have:

x = -3

Therefore, the solution set for the equation 5(x-2)^2 = 125 is x = -3 or x = 7.

Regarding your question about where the -20x + 20 term came from, it seems there might be a misunderstanding. There is no -20x + 20 in the given equation. The equation 5(x-2)^2 = 125 simplifies to (x-2)^2 = 25.