Question

Solve x2 + 4x – 4 = 8 for x.

A. –6 or x = 2
B. x= -2 + or - 2 with a square root of 2
C. x = –2 or x = 6
D. x= 2 + or - 2 with a square root of 2

Answer 1

A. x=-6 or x=2
Quadratic equation

Answer 2

we know that

To find the solution let's factor the equation

`x^(2) + 4x - 4 = 8`

Group terms that contain the same variable, and move the constant to the opposite side of the equation

`x^(2) + 4x = 8+4`

`x^(2) + 4x = 12`

Complete the square. Remember to balance the equation by adding the same constants to each side

`x^(2) + 4x+4 = 12+4`

`x^(2) + 4x+4 = 16`

Rewrite as perfect squares

`(x+2)^(2) = 16`

`(x+2)^(2) = 16\\ (x+2)=(+/-)√(16) \\ x1=-2+√(16) =-2+4=2\\ x2=-2-√(16) =-2-4=-6`

therefore

the answer is the option

A. –6 or x = 2