ANSWER
![x = - 2 \pm i](https://tex.z-dn.net/?f=x%20%3D%20-%202%20%5Cpm%20i)
EXPLANATION
We use the method of completing the squares.
The equation is
![3 {x}^{2} = - 12x - 15](https://tex.z-dn.net/?f=3%20%7Bx%7D%5E%7B2%7D%20%3D%20-%2012x%20-%2015)
We rewrite the above equation to obtain;
![3 {x}^{2} + 12x = - 15](https://tex.z-dn.net/?f=3%20%7Bx%7D%5E%7B2%7D%20%2B%2012x%20%3D%20-%2015)
We divide through by 3 to obtain;
![{x}^{2} + 4x = - 5](https://tex.z-dn.net/?f=%20%7Bx%7D%5E%7B2%7D%20%2B%204x%20%3D%20-%205)
We add half the coefficient of
![x](https://tex.z-dn.net/?f=x)
to both sides of the equation to get,
![{x}^{2} + 4x + {2}^{2} = - 5 + {2}^{2}](https://tex.z-dn.net/?f=%20%7Bx%7D%5E%7B2%7D%20%2B%204x%20%2B%20%7B2%7D%5E%7B2%7D%20%3D%20-%205%20%2B%20%7B2%7D%5E%7B2%7D%20)
The right hand side is now a perfect square.
![{(x + 2)}^{2} = - 1](https://tex.z-dn.net/?f=%7B%28x%20%2B%202%29%7D%5E%7B2%7D%20%3D%20-%201)
We now take square root of both sides to get;
![x + 2 = \pm \sqrt{ - 1}](https://tex.z-dn.net/?f=x%20%2B%202%20%3D%20%5Cpm%20%5Csqrt%7B%20-%201%7D%20)
We add -2 to both sides,
![x = - 2 \pm \sqrt{ - 1}](https://tex.z-dn.net/?f=x%20%3D%20-%202%20%5Cpm%20%5Csqrt%7B%20-%201%7D%20)
We simplify to obtain,
Answer:
x-4
Step-by-step explanation:
According to me the probability is 1/4, because there are 4 possible outcomes when two coins are flipped - TT, TH, HT, HH.
<span>Also, would it matter if the coins are flipped one after other rather than together</span>
Answer:
40
Step-by-step explanation:
![\left[\begin{array}{ccc}a&b\\c&d\end{array}\right] = ad-bc](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Da%26b%5C%5Cc%26d%5Cend%7Barray%7D%5Cright%5D%20%3D%20ad-bc)