Use the quadratic formula to solve \( 2 x^{2}-4=0 \) \( x=\square \) Basic Funcs Trig

To solve the equation \( 2x^2 - 4 = 0 \), we first rearrange it into standard form: \( 2x^2 = 4 \). Dividing both sides by 2 gives \( x^2 = 2 \). Taking the square root of both sides results in \( x = \pm\sqrt{2} \). Therefore, the solutions are \( x = \sqrt{2} \) and \( x = -\sqrt{2} \). Now, if we were to use the quadratic formula \( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \) with \( a = 2 \), \( b = 0 \), and \( c = -4 \), we’d compute it as follows: \( b^2 - 4ac = 0^2 - 4(2)(-4) = 32 \). Plugging it in gives \( x = \frac{0 \pm \sqrt{32}}{4} = \frac{\pm 4\sqrt{2}}{4} = \pm \sqrt{2} \), confirming our result.