If using the method of completing the square to solve the quadratic equation x, squared, plus, 9, x, plus, 35, equals, 0*x*2+9*x*+35=0, which number would have to be added to "complete the square"?

To solve the quadratic equation \(x^2 + 9x + 35 = 0\) using the method of completing the square, we need to manipulate the equation so that it forms a perfect square trinomial. 

### Step 1: Isolate the quadratic and linear terms
First, let's focus on the \(x^2\) and \(9x\) terms:

\[
x^2 + 9x
\]

### Step 2: Determine the number to complete the square
To complete the square, take half of the coefficient of \(x\) (which is 9), then square it:

\[
\left(\frac{9}{2}\right)^2 = \left(\frac{9}{2}\right) \times \left(\frac{9}{2}\right) = \frac{81}{4}
\]

### Final Answer:
The number that would have to be added to \(x^2 + 9x\) to complete the square is \(\frac{81}{4}\).

Would you like more details or have any questions?

Here are 5 related questions:
1. How does completing the square help solve quadratic equations?
2. What is the next step after completing the square when solving the equation?
3. How does the method of completing the square compare to using the quadratic formula?
4. What is the geometric interpretation of completing the square?
5. Can completing the square be used to derive the quadratic formula?

**Tip:** Completing the square is particularly useful when solving quadratic equations that don't factor easily or when trying to convert a quadratic equation into vertex form.

Learn how to solve the quadratic equation x^2 + 9x + 35 = 0 by completing the square. Understand the steps involved and the number needed to complete the square. Suitable for high school students studying algebra and quadratic equations.

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