To complete the square for the polynomial \( j^2 + 20j \), we can follow these steps:
-
Take the coefficient of the linear term (which is 20), divide it by 2, and then square it.
- \(\frac{20}{2} = 10\)
- \(10^2 = 100\)
-
Add and subtract this squared value (100) to the polynomial: \[ j^2 + 20j + 100 - 100 \] This can be rewritten as: \[ (j^2 + 20j + 100) - 100 \]
-
The expression \( j^2 + 20j + 100 \) can be factored as a perfect square: \[ (j + 10)^2 - 100 \]
Therefore, the number that makes the polynomial \( j^2 + 20j \) a perfect-square quadratic is 100.
Thus, the completed expression is: \[ j^2 + 20j + 100 \]