Question

If using the method of completing the square to solve the quadratic equation x, squared, plus, 9, x, plus, 35, equals, 0x
2
+9x+35=0, which number would have to be added to "complete the square"?
Answer
Attempt 1 out of 5

Answer 1

To complete the square for the quadratic equation \(x^2 + 9x + 35 = 0\), we first focus on the quadratic and linear terms: \(x^2 + 9x\).

1. Take the coefficient of \(x\), which is 9.
2. Divide it by 2: \(\frac{9}{2} = 4.5\).
3. Square that result: \(4.5^2 = 20.25\).

Thus, the number that must be added (and subtracted) to complete the square is \(20.25\).

So, we add \(20.25\) to both sides of the equation:

\[
x^2 + 9x + 20.25 - 20.25 + 35 = 0
\]
which simplifies to:

\[
(x + 4.5)^2 - 20.25 + 35 = 0
\]

In conclusion, the number that would have to be added to complete the square is **20.25**.