Using the difference of squares pattern, find the two values that solve the following equation: (3x−9)2=36. Put the answers in order from least to greatest.(1 point)

Answer 1

To solve the equation \( (3x - 9)^2 = 36 \) using the difference of squares pattern, we can start by taking the square root of both sides.

1. Take the square root of both sides: \[ 3x - 9 = \pm 6 \]

This gives us two separate equations to solve:

Case 1: \[ 3x - 9 = 6 \]

Add 9 to both sides: \[ 3x = 15 \]

Now, divide by 3: \[ x = 5 \]

Case 2: \[ 3x - 9 = -6 \]

Add 9 to both sides: \[ 3x = 3 \]

Now, divide by 3: \[ x = 1 \]

Now we have our two solutions: \( x = 5 \) and \( x = 1 \).

Putting them in order from least to greatest: The solutions are: \[ \boxed{1} \quad \text{and} \quad \boxed{5} \]