Question

solve by quadratic formula. x squared plus x plus 1 = 0

Answer 1

Remember that the quadratic formula is: $\dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$.

$a$ stands for the coefficient of the first term, the one associated with the $x^2$, $b$ stands for the coefficient of the second term, the one associated with $x$, and $c$ stands for the value of the constant.

In $x^2 + x + 1 = 0$, our a-value is 1, our b-value is also 1, and our c-value is also 1.

Thus, when we plug in our values into our formula, we get the answer:

$\dfrac{-1 \pm \sqrt{1^2 - 4(1)(1)}}{2(1)} = \dfrac{-1 \pm \sqrt{-3}}{2}$

Simplifying this answer using $i = \sqrt{-1}$, we get our final answer of:

$\boxed{x = \dfrac{-1 \pm i\sqrt{3}}{2}}$