Question

What equation results from completing the square and then factoring x^+4x=7

Answer 1

Given equation:
`x^2+4x =7`

when we complete the square , we take half of the value of 4 , then square it, and added to the left sides, we get;

`x^2+4x+2^2 = 7+2^2`

∵4 is the value
`((4)/(2))^2`

Notice, that we add this both sides so that it maintains the equality.

then;

`x^2+4x+2^2 = 7+2^2`

`(x+2)^2 = 7+ 4` [
`(a+b)^2 = a^2+2ab+b^2` ]

Simplify:

`(x+2)^2 =11`

Therefore, the equation result is,
`(x+2)^2 =11`

Answer 2

The resulting equation is (x + 2)^2 = 11

Explanation:

It is given that, x^2 + 4x=7 ----(1)

The quadratic equation is of the form ax^2 + bx + c = 0

in completing square method we have to add( b/2)² in both the sides

In eq (1) b = 4, then b/2 = 4/2 = 2

Therefore we have to add 2^2 = 4 in both sides of the eq (1)

eq (1) becomes x^2 + 4x + 4=7 + 4

x^2 + 4x + 4 = 11

(x + 2)^2 = 11

Therefore the resulting equation is

(x + 2)^2 = 11