What number would you add to both sides of x2 – 20x = 5 to complete the square?

Answer 1

To complete the square for the quadratic equation \( x^2 - 20x = 5 \), we need to focus on the expression on the left side, \( x^2 - 20x \).

1. Start by taking the coefficient of \( x \), which is \(-20\).
2. Divide that coefficient by \( 2 \): \[ -20 \div 2 = -10 \]
3. Square the result: \[ (-10)^2 = 100 \]

So, to complete the square, you would add \( 100 \) to both sides of the equation. This gives you:

\[ x^2 - 20x + 100 = 5 + 100 \]

Simplifying the right side:

\[ x^2 - 20x + 100 = 105 \]

Thus, the number you would add to both sides to complete the square is 100.