solve the quadratic equation.\n2x² + 4x - 1 = 0\nwrite one exact solution in each box. you can add or remove…

Explanation:

Step1: Identify coefficients

For the quadratic equation $2x^{2}+4x - 1=0$, we have $a = 2$, $b = 4$, $c=-1$.

Step2: Apply quadratic formula

The quadratic formula is $x=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}$. Substitute $a = 2$, $b = 4$, $c=-1$ into it: [ \begin{align*} x&=\frac{-4\pm\sqrt{4^{2}-4\times2\times(-1)}}{2\times2}\ &=\frac{-4\pm\sqrt{16 + 8}}{4}\ &=\frac{-4\pm\sqrt{24}}{4}\ &=\frac{-4\pm2\sqrt{6}}{4}\ &=\frac{-2\pm\sqrt{6}}{2} \end{align*} ]

Answer:

$x=\frac{-2+\sqrt{6}}{2}$, $x=\frac{-2 - \sqrt{6}}{2}$