QuestionWhat are the solutions to $2 x^{2}+8 x+4=0$ ? $x=-6 \pm \sqrt{2}$ $x=-6 \pm 6 \sqrt{2}$ $x=-2 \pm \sqrt{2}$ $x=-2 \pm \frac{\sqrt{30}}{3}$

Studdy Solution
Calculate the solutions using the quadratic formula:
Substitute the simplified discriminant back into the quadratic formula:
$$x = \frac{-8 \pm \sqrt{32}}{4}$$
Simplify $\sqrt{32}$:
$$\sqrt{32} = \sqrt{16 \cdot 2} = 4\sqrt{2}$$
Substitute back:
$$x = \frac{-8 \pm 4\sqrt{2}}{4}$$
Simplify the expression:
$$x = \frac{-8}{4} \pm \frac{4\sqrt{2}}{4}$$ $$x = -2 \pm \sqrt{2}$$
The solutions to the equation are:
$$x = -2 \pm \sqrt{2}$$