Solve x2 + 4x = 4 for x by completing the square.

A. X=-4

B. X=0

C. X = ± square root of 8 + 2

D. X = ± square root of 8 - 2

D. X = ± square root of 8 - 2

Step-by-step explanation:

Given quadratic equation is / [x^{2}+4x=4/]

Rearranging the terms: / [x^{2}+4x-4=0/]

This is the standard format of quadratic equation of the form / [ax^{2}+bx+c=0/]

Here, a=1, b=4 and c=-4.

Roots of the quadratic equation are given by / [/frac{-b / pm / sqrt{b^{2}-4ac}}{2a}/]

Substituting the values and calculating the roots:

/[/frac{-4 / pm / sqrt{ (-4) ^{2}-4*1 * (-4)) }}{2*1}/]

= / [/frac{-4 / pm / sqrt{32}}{2}/]

= / [/frac{-2*2 / pm 2*/sqrt{8}}{2}/]

= / [-2 / pm / sqrt{8}/]

Hence option D is the correct option.