Question

What number should be added to both sides of the equation to complete the square? X^2-6xx=5

Answer 1

9

Explanation:

`x^2-6x = 5\\`

We know the binomial formula:
`(a-b)^2 = a^2 -2ab + b^2`

Let's consider 6x = 2ab, we know a is our first term - x;

6x = 2axb

6 = 2b

b = 3

So to make a perfect square, we need to add
`b^2` to both sides

`x^2 - 6x + 3^2 = 5 + 3^2\\x^2 - 6x + 9 = 5 + 9\\(x-3)^2 = 14`

Answer 2

9

Explanation:

To complete the square, divide the coefficient of the b term 6x in two. This becomes -6/2=-3. Now square the number -3 and it becomes 9. To complete the square add 9 to both sides.