solve the quadratic equation.\n7x² + 2x + 1 = 0\nwrite one exact solution in each box. you can add or remove…

Answer:

$x=\frac{-2\pm\sqrt{4 - 28}}{14}=\frac{-2\pm\sqrt{- 24}}{14}=\frac{-2\pm2\sqrt{6}i}{14}=\frac{-1\pm\sqrt{6}i}{7}$

Explanation:

Step1: Identify coefficients

For the quadratic equation $ax^{2}+bx + c = 0$, here $a = 7$, $b = 2$, $c = 1$.

Step2: Calculate the discriminant

The discriminant $\Delta=b^{2}-4ac$. Substitute the values: $\Delta=(2)^{2}-4\times7\times1=4 - 28=-24$.

Step3: Apply the quadratic formula

The quadratic formula is $x=\frac{-b\pm\sqrt{\Delta}}{2a}$. Substitute $a = 7$, $b = 2$, $\Delta=-24$: $x=\frac{-2\pm\sqrt{-24}}{14}$. Simplify $\sqrt{-24}=2\sqrt{6}i$, then $x=\frac{-2\pm2\sqrt{6}i}{14}=\frac{-1\pm\sqrt{6}i}{7}$.