Question

the solution of $7x^2 + 2x + 3 = -1$?
options:
a. $\frac{-1pm2isqrt{5}}{7}$
b. $\frac{1pm3isqrt{3}}{7}$
c. $\frac{-1pm3isqrt{3}}{7}$
d. $\frac{1pm2isqrt{5}}{7}$

Explanation:

Step1: Rewrite to standard quadratic form

$7x^2 + 2x + 3 + 1 = 0$
$7x^2 + 2x + 4 = 0$

Step2: Identify coefficients

For $ax^2+bx+c=0$, $a=7$, $b=2$, $c=4$

Step3: Use quadratic formula

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$
Substitute values:
$x=\frac{-2\pm\sqrt{2^2-4\times7\times4}}{2\times7}$

Step4: Calculate discriminant

$\sqrt{4-112}=\sqrt{-108}=\sqrt{36\times(-3)}=6i\sqrt{3}$

Step5: Simplify the expression

$x=\frac{-2\pm6i\sqrt{3}}{14}=\frac{-1\pm3i\sqrt{3}}{7}$

Answer:

C. $\frac{-1\pm3i\sqrt{3}}{7}$