`(2-sqrt(-25))(-7+sqrt(-4))=x+yi`
In the equation above, what is the value of y?

Answer

To solve the equation \((2-\sqrt{-25})(-7+\sqrt{-4})=x+yi\), we will follow these steps:

### Step 1: Simplify the square roots
First, we need to simplify the square roots of the negative numbers:
- \(\sqrt{-25} = \sqrt{25} \cdot \sqrt{-1} = 5i\)
- \(\sqrt{-4} = \sqrt{4} \cdot \sqrt{-1} = 2i\)

### Step 2: Substitute the simplified values into the expression
Now, we substitute these values back into the expression:
\[ (2 - 5i)(-7 + 2i) \]

### Step 3: Use the distributive property (FOIL)
Next, we will apply the distributive property (also known as the FOIL method) to expand the expression:
\[ = 2 \cdot (-7) + 2 \cdot (2i) - 5i \cdot (-7) - 5i \cdot (2i) \]
Calculating each term:
- \(2 \cdot (-7) = -14\)
- \(2 \cdot (2i) = 4i\)
- \(-5i \cdot (-7) = 35i\)
- \(-5i \cdot (2i) = -10i^2\)

### Step 4: Substitute \(i^2 = -1\)
Since \(i^2 = -1\), we can substitute:
\[ -10i^2 = -10(-1) = 10 \]

### Step 5: Combine all the terms
Now we combine all the terms:
\[ -14 + 4i + 35i + 10 \]
Combining the real parts and the imaginary parts:
\[ (-14 + 10) + (4i + 35i) = -4 + 39i \]

### Step 6: Identify \(x\) and \(y\)
Now we can express our result in the form \(x + yi\):
\[ -4 + 39i \]
From this, we can see that:
- \(x = -4\)
- \(y = 39\)

### Final Answer
Thus, the value of \(y\) is:
\[ \boxed{39} \]