Question

solve for x in the equation (x^2 + 4x - 4 = 0)
(x = -6) or (x = 2)
(x = -2 pm 2sqrt{2})
(x = -2) or (x = 6)
(x = 2 pm 2sqrt{2})

Explanation:

Step1: Identify quadratic form

The equation is $x^2 + 4x - 4 = 0$, which matches $ax^2+bx+c=0$ where $a=1$, $b=4$, $c=-4$.

Step2: Apply quadratic formula

Use $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$.
Substitute values: $x=\frac{-4\pm\sqrt{4^2-4(1)(-4)}}{2(1)}$

Step3: Calculate discriminant

Compute $\sqrt{16 + 16}=\sqrt{32}=4\sqrt{2}$

Step4: Simplify the expression

$x=\frac{-4\pm4\sqrt{2}}{2}=-2\pm2\sqrt{2}$

Answer:

$x=-2\pm2\sqrt{2}$ (matches the second option: $x=-2\pm2\sqrt{2}$)