solve the quadratic equation. -5x² + 6x - 2 = 0 write one exact solution in each box. you can add or remove…

Explanation:

Step1: Identify coefficients

For the quadratic equation $-5x^{2}+6x - 2=0$, we have $a=-5$, $b = 6$, $c=-2$.

Step2: Calculate the discriminant

The discriminant $\Delta=b^{2}-4ac$. Substitute the values: $\Delta=(6)^{2}-4\times(-5)\times(-2)=36 - 40=-4$.

Step3: Use the quadratic - formula

The quadratic formula is $x=\frac{-b\pm\sqrt{\Delta}}{2a}$. Since $\Delta=-4<0$, there are no real solutions. In the complex - number system, $x=\frac{-6\pm\sqrt{- 4}}{2\times(-5)}=\frac{-6\pm2i}{-10}=\frac{3\pm i}{5}$. One exact solution is $x=\frac{3 + i}{5}$.

Answer:

$\frac{3 + i}{5}$