Question

for the few questions in this set, you will see the quadratic formula. soon, you will need to answer the questions without this reminder.
$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ for $ax^2 + bx + c = 0$
solve for $x$. write both solutions, separated by a comma.
$3x^2 - x - 14 = 0$
enter the correct answer.

Explanation:

Step1: Identify a, b, c values

From $3x^2 - x - 14 = 0$, we get $a=3$, $b=-1$, $c=-14$.

Step2: Calculate discriminant

$\Delta = b^2 - 4ac = (-1)^2 - 4(3)(-14) = 1 + 168 = 169$

Step3: Substitute into quadratic formula

$x = \frac{-b \pm \sqrt{\Delta}}{2a} = \frac{-(-1) \pm \sqrt{169}}{2(3)} = \frac{1 \pm 13}{6}$

Step4: Solve for both x values

First solution: $x = \frac{1 + 13}{6} = \frac{14}{6} = \frac{7}{3}$
Second solution: $x = \frac{1 - 13}{6} = \frac{-12}{6} = -2$

Answer:

$x=-2, x=\frac{7}{3}$