solve the quadratic equation.\n5x² + 4x + 1 = 0\nwrite one exact solution in each box. you can add or remove…

Explanation:

Step1: Identify coefficients

For the quadratic equation $5x^{2}+4x + 1=0$, $a = 5$, $b = 4$, $c = 1$.

Step2: Calculate the discriminant

The discriminant $\Delta=b^{2}-4ac$. Substitute the values: $\Delta=(4)^{2}-4\times5\times1=16 - 20=-4$.

Step3: Use the quadratic - formula

The quadratic formula is $x=\frac{-b\pm\sqrt{\Delta}}{2a}$. Since $\Delta=-4\lt0$, the solutions are complex numbers. $x=\frac{-4\pm\sqrt{-4}}{2\times5}=\frac{-4\pm2i}{10}=\frac{-2\pm i}{5}$. One solution is $x=\frac{-2 + i}{5}$, and the other is $x=\frac{-2 - i}{5}$. We can write one of them, for example:

Answer:

$x=\frac{-2 + i}{5}$