Question

Math

Posted 5 months ago

```
Find the solutions of the quadratic equation $6 x^{2}-6 x-2=0$.
Choose 1 answer:
(A) $-\frac{1}{2} \pm \frac{\sqrt{21}}{6} i$
(B) $\frac{1}{2} \pm \frac{\sqrt{21}}{6} i$
(C) $\frac{1}{2} \pm \frac{\sqrt{21}}{6}$
(D) $-\frac{1}{2} \pm \frac{\sqrt{21}}{6}$
```

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Answer from Sia

Posted 5 months ago

Solution by Steps

step 2

Here, $a = 6$, $b = -6$, and $c = -2$. Plugging these values into the quadratic formula gives us $x = \frac{-(-6) \pm \sqrt{(-6)^2 - 4(6)(-2)}}{2(6)}$

step 3

Simplifying inside the square root gives us $x = \frac{6 \pm \sqrt{36 + 48}}{12}$

step 4

Further simplification of the square root gives us $x = \frac{6 \pm \sqrt{84}}{12}$

step 5

Simplifying $\sqrt{84}$ to $2\sqrt{21}$, we get $x = \frac{6 \pm 2\sqrt{21}}{12}$

step 6

Dividing numerator and denominator by 2 gives us $x = \frac{3 \pm \sqrt{21}}{6}$

C

Key Concept

Quadratic Formula

Explanation

To find the roots of a quadratic equation $ax^2 + bx + c = 0$, the quadratic formula $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ is used. After simplifying, we get the solutions for $x$.

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