In each of the following find the value of 'a'
`4x^(2) + ax + 9 = (2x-3)^(2)`

Answer

To solve the equation \(4x^2 + ax + 9 = (2x - 3)^2\) and find the value of \(a\), we will follow these steps:

### Step 1: Expand the right-hand side
We start by expanding the expression on the right-hand side using the formula for the square of a binomial, which states that \((a - b)^2 = a^2 - 2ab + b^2\).

\[ (2x - 3)^2 = (2x)^2 - 2(2x)(3) + (3)^2 \]

Calculating this gives:

\[ = 4x^2 - 12x + 9 \]

### Step 2: Set the equation
Now we can rewrite the original equation with the expanded form:

\[ 4x^2 + ax + 9 = 4x^2 - 12x + 9 \]

### Step 3: Cancel out common terms
Next, we can subtract \(4x^2\) and \(9\) from both sides of the equation:

\[ ax = -12x \]

### Step 4: Solve for \(a\)
Now, we can isolate \(a\) by dividing both sides by \(x\) (assuming \(x \neq 0\)):

\[ a = -12 \]

Thus, the value of \(a\) is \(-12\).

### Final Answer:
\[ a = -12 \]

---