In the equation `(ax + 3)^2` = 36, a is a constant. If x = −3 is one solution to the equation, what is a possible value of a ?

Options

A. `-11`
B. `-5`
C. `-1`
D. 0

Explanation

To solve the equation \((ax + 3)^2 = 36\) given that \(x = -3\) is one solution, we can follow these steps:

### Step 1: Substitute \(x = -3\) into the equation
We start by substituting \(x = -3\) into the equation:
\[ (ax + 3)^2 = 36 \]
This becomes:
\[ (a(-3) + 3)^2 = 36 \]

### Step 2: Simplify the equation
Now, simplify the expression inside the parentheses:
\[ (-3a + 3)^2 = 36 \]

### Step 3: Take the square root of both sides
Next, we take the square root of both sides. Remember that taking the square root introduces a positive and negative solution:
\[ -3a + 3 = 6 \quad \text{or} \quad -3a + 3 = -6 \]

### Step 4: Solve the first equation
Let's solve the first equation:
\[ -3a + 3 = 6 \]
Subtract 3 from both sides:
\[ -3a = 3 \]
Now, divide by -3:
\[ a = -1 \]

### Step 5: Solve the second equation
Now, let's solve the second equation:
\[ -3a + 3 = -6 \]
Subtract 3 from both sides:
\[ -3a = -9 \]
Now, divide by -3:
\[ a = 3 \]

### Step 6: Conclusion
Thus, the possible values of \(a\) are \(a = -1\) and \(a = 3\).