how do i complete the square on this problem: x^2-16x+48 ?

Answer 1

Look at the number in front of the single x. Take that number, divide it by two, then square the result.

16 / 2 = 8
8^2 = 64

That's the number you need to add and subtract from the expression.

x^2 - 16x + 48
= x^2 - 16x + 64 - 64 + 48
= (x^2 - 16x + 64) + (48 - 64)
= (x - 8)^2 - 16

Answer 2

To complete the square, i.e. construct a perfect square trinomial, divide the coefficient of x by 2, square it, and add it to the original expression. In this problem, -16/2 = 8, then 8^2=64. If we then add 64 to the expression, we must also subtract 64 to maintain balance.

(x^2 - 16x + 64) + 48 - 64

We go to this process in order to be able to factor x^2 - 16x + 64; this comes out to (x-8)(x-8), or as you can see, (x-8)^2, a perfect square. The rest is a matter of combining like terms:

(x-8)^2 - 16.

This process works when the coefficient of x^2 is 1. For a problem such as 2x^2 + 6x + 9, it would be necessary to factor out the two and then proceed as shown above.

Hope this helps.

Answer 3

x^2-16x+48 +16-16
x^2-16x+64-16
(x-8)^2-16

Answer 4

(x² - 16x + 64) - 64 + 48
(x - 8)² - 16

Answer 5

x^2-16x+48 +16-16
x^2-16x+64-16
(x-8)^2-16