Question

What number should be added to both sides of the equation to complete the square x^2+8x=4​

Answer 1

It would be half of the coefficient of x squared added to both sides:
So half of 8 ( the coefficient of 8x) is 4;
The number 4 squared is 16, so you would add that to both sides.

You do this so that you can easily factor the left side: x^2 + 8x + 16 = 4 + 16
(x + 4)(x+4) = 20

Answer 2

To complete the square you have to add 20.

Explanation:

The concept of square of a binomial can be represented as

(a + b)² = a² + b² + 2ab

Then given x² + 8x = 4 ⇒ x² + 8x -4 = 0. From this expression we can easy identify "a" as x. Then b can be obtained if we think that 2ab=8x

⇒2xb=8x ⇒b = 8x/2x ⇒b=4.

As you can see if a=x and b=4, then you have (x + 4)²

⇒(x + 4)²= x² + 16 + 8x.

Finally if the final expression is x² + 16 + 8x, you have to add 20 to the given expression.

x² + 8x - 4 + 20 = x² + 8x + 16.