Can someone walk me through this?

Question

What is the missing constant term in the perfect square that starts with x2−20x

Answer 1

Completing the square is based on the idea that (x + a)² is equal to x² + 2ax + a^2. (x + a)² is the perfect square that you want to complete by adding a constant that is determined by the x term of the original expression.

To find the value of a, notice that the middle term of the expanded expression is twice the value of a. So use one half the coffecient of the x term, then square that to get a², which is what you need to add to complete the square.

In this example, you start with x² - 20x. If there were a coefficient in front x² you would have to divide by that coefficient first. But you do not have one, so no need this time. The coefficient for x is -20, so 1/2 of that is equal to a, or -10. But what you need to add is a², so square that to get 100. Adding that to the first expression gives x² -20x + 100. That factors to (x-10)², which is a perdect square.

When you use this to solve the quadratic, don't forget to subtract 100 from the right side of the equation to keep it balanced,

Hope this helps

Answer 2

Since this is a perfect square, we can complete the square on the two terms that are given to determine the constant term. We do this by taking half the coefficient of the "x" term, so -20 divided by 2, and this equals -10. Then we square this amount, (-10)² = 100, and we let this be the constant, inserting it with a plus sign since it is a positive 100. So the perfect square trinomial is x² - 20x + 100 and the constant term is 100.