Question

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:
\[
\boxed{1} \quad \text{and} \quad \boxed{5}
\]