What number must you add to complete the square and then factoring x^2+4x=7

+ 4

Step-by-step explanation:

given

x² + 4x = 7

To complete the square

add ( half the coefficient of the x- term )² to both sides

x² + 4x + ()² = 7 + ()², that is

x² + 4x + 4 = 7 + 4

(x + 2)² = 11

The  number 4 must add to complete the square

(x + 2)^2 = 11

Step-by-step explanation:

The given quadratic equation is, x^2 + 4x = 7

For completing square,

We have to add square of half of the coefficient of x.

Here coefficient of x is 4

Half of coefficient of x = 4/2 = 2

Square of half of coefficient of x = 2^2 = 4

We have to add 4 on both side

Therefore the answer is 4

Factoring  x^2 + 4x = 7

Add 4 on both side we get,

x^2 + 4x  + 4 = 7 + 4

(x + 2)^2 = 11

(1,4) is on graph of f(x)

f(1) = 4

so 1/4 f(x)

1/4 f(1)

1/4. ×4

1

so point for function 1/4. f(x) is (1,1)