Question

solve the quadratic equation $5x^2 + 2x + 1 = 0$. use the keypad to enter the answer as a single simplified expression in the box. $x = \square$

Explanation:

Step1: Identify quadratic coefficients

For $ax^2+bx+c=0$, here $a=5$, $b=2$, $c=1$.

Step2: Calculate discriminant

$\Delta = b^2-4ac = 2^2 - 4(5)(1) = 4-20=-16$

Step3: Apply quadratic formula

$x=\frac{-b\pm\sqrt{\Delta}}{2a}=\frac{-2\pm\sqrt{-16}}{10}$

Step4: Simplify imaginary root

$\sqrt{-16}=4i$, so $x=\frac{-2\pm4i}{10}=\frac{-1\pm2i}{5}$

Answer:

$x=\frac{-1+2i}{5}$ and $x=\frac{-1-2i}{5}$