hope it helps you!!!!!!!!!!
Since it’s indicated that BC and AD are congruent, you can set the two sides/equations equal to one another:
3x+3=x+21
Then, you can solve for x:
3x+3=x+21
2x=18
x=9
Plugging in 9 into either equation of BC or AD should give you 30 for both sides:
3(9)+3=30
(9)+21=30
For CD, you can also plug in 9 for x:
2(9)-9=18
Since AB and CD are labeled as congruent, both sides are 18.
x=9
AB=18
BC=30
CD=18
AD=30
Given:
![a^2+3a+9=0](https://tex.z-dn.net/?f=a%5E2%2B3a%2B9%3D0)
If we need to find what
is, we can solve for a and plug it in. Let's use the quadratic formula to solve for a. The quadratic formula is:
and ![a=\frac{-b-\sqrt{b^2-4ac}}{2a}](https://tex.z-dn.net/?f=a%3D%5Cfrac%7B-b-%5Csqrt%7Bb%5E2-4ac%7D%7D%7B2a%7D)
Let's identify our a, b, and c:
a: 1
b: 3
c: 9
Plug in the values into the quadratic formula:
![a=\frac{-3+\sqrt{(3)^2-4(1)(9)}}{2(1)}](https://tex.z-dn.net/?f=a%3D%5Cfrac%7B-3%2B%5Csqrt%7B%283%29%5E2-4%281%29%289%29%7D%7D%7B2%281%29%7D)
Simplify everything under the radical:
![a=\frac{-3+\sqrt{-27}}{2}](https://tex.z-dn.net/?f=a%3D%5Cfrac%7B-3%2B%5Csqrt%7B-27%7D%7D%7B2%7D)
Simplify the radical:
![a=\frac{-3+3i\sqrt{3}}{2}](https://tex.z-dn.net/?f=a%3D%5Cfrac%7B-3%2B3i%5Csqrt%7B3%7D%7D%7B2%7D)
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Let's solve for the second part of the quadratic formula. Everything will be the same, so we can just replace the + with a -.
and ![a=\frac{-3-3i\sqrt{3}}{2}](https://tex.z-dn.net/?f=a%3D%5Cfrac%7B-3-3i%5Csqrt%7B3%7D%7D%7B2%7D)
These two are your answers. Now, since we know what a is, let's cube this value:
![(a=\frac{-3+3i\sqrt{3}}{2})^3](https://tex.z-dn.net/?f=%28a%3D%5Cfrac%7B-3%2B3i%5Csqrt%7B3%7D%7D%7B2%7D%29%5E3)
Simplify:
![27](https://tex.z-dn.net/?f=27)
You will get the same answer if you cube both of the quadratic answers. So, your final answer:
![a^3=27](https://tex.z-dn.net/?f=a%5E3%3D27)