Question

If using the method of completing the square to solve the quadratic equation x, squared, plus, 20, x, minus, 6, equals, 0x
2
+20x−6=0, which number would have to be added to "complete the square"?

Answer 1

To complete the square for the quadratic equation \( x^2 + 20x - 6 = 0 \), we need to focus on the \( x^2 + 20x \) part.

1. Take the coefficient of \( x \), which is \( 20 \).
2. Divide this coefficient by \( 2 \):
\[
\frac{20}{2} = 10
\]
3. Square this result:
\[
10^2 = 100
\]

We need to add \( 100 \) to both sides of the equation to complete the square.

So, the completed square form of the equation will be:
\[
x^2 + 20x + 100 - 6 = 100
\]
or
\[
(x + 10)^2 - 6 = 100.
\]

In summary, the number that must be added to complete the square is **100**.