If using the method of completing the square to solve the quadratic equation x, squared, plus, 20, x, minus, 6, equals, 0x

Question

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.