ANSWER
![x=\frac{2-\sqrt{10}} {3}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B2-%5Csqrt%7B10%7D%7D%20%7B3%7D)
or
![x=\frac{\sqrt{10}+2} {3}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B%5Csqrt%7B10%7D%2B2%7D%20%7B3%7D)
We have
![3x^2-4x-2=0](https://tex.z-dn.net/?f=3x%5E2-4x-2%3D0)
Since we cannot factor easily, we complete the square.
Adding 2 to both sides give,
![3x^2-4x=2](https://tex.z-dn.net/?f=3x%5E2-4x%3D2)
Dividing through by 3 gives
![x^2-\frac{4}{3}x= \frac{2}{3}](https://tex.z-dn.net/?f=x%5E2-%5Cfrac%7B4%7D%7B3%7Dx%3D%20%5Cfrac%7B2%7D%7B3%7D)
Adding
![(-\frac{2}{3})^2](https://tex.z-dn.net/?f=%28-%5Cfrac%7B2%7D%7B3%7D%29%5E2)
to both sides gives
![x^2-\frac{4}{3}x+(-\frac{2}{3})^2= \frac{2}{3}+(-\frac{2}{3})^2](https://tex.z-dn.net/?f=x%5E2-%5Cfrac%7B4%7D%7B3%7Dx%2B%28-%5Cfrac%7B2%7D%7B3%7D%29%5E2%3D%20%5Cfrac%7B2%7D%7B3%7D%2B%28-%5Cfrac%7B2%7D%7B3%7D%29%5E2)
The expression on the Left Hand side is a perfect square.
![(x-\frac{2}{3})^2= \frac{2}{3}+\frac{4}{9}](https://tex.z-dn.net/?f=%28x-%5Cfrac%7B2%7D%7B3%7D%29%5E2%3D%20%5Cfrac%7B2%7D%7B3%7D%2B%5Cfrac%7B4%7D%7B9%7D)
![\Rightarrow (x-\frac{2}{3})^2= \frac{10}{9}](https://tex.z-dn.net/?f=%5CRightarrow%20%28x-%5Cfrac%7B2%7D%7B3%7D%29%5E2%3D%20%5Cfrac%7B10%7D%7B9%7D)
![\Rightarrow (x-\frac{2}{3})=\pm \sqrt{\frac{10}{9}}](https://tex.z-dn.net/?f=%5CRightarrow%20%28x-%5Cfrac%7B2%7D%7B3%7D%29%3D%5Cpm%20%5Csqrt%7B%5Cfrac%7B10%7D%7B9%7D%7D)
![\Rightarrow (x)=\frac{2}{3} \pm {\frac{\sqrt{10}}{3}](https://tex.z-dn.net/?f=%5CRightarrow%20%28x%29%3D%5Cfrac%7B2%7D%7B3%7D%20%5Cpm%20%7B%5Cfrac%7B%5Csqrt%7B10%7D%7D%7B3%7D)
Splitting the plus or minus sign gives
![x=\frac{2- \sqrt{10}} {3}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B2-%20%5Csqrt%7B10%7D%7D%20%7B3%7D)
or
Answer:
4:9
Step-by-step explanation:
- Circles: 8
- Total shapes: squares + circles
- Total shapes: 10 + 8
- Total shapes: 18
- Circles : Total shapes = 8:18
- 8:18 = 4:9
I hope this helps!
Answer:
If you aren't looking for the quadratic solving method then comment it down below and tell me what you're looking for
QUADRATIC EQUATION
x²- 4x = 6
(x - 2)²- 4 = 6
(x - 2)² = 10
x - 2 = ±10
x = ±10+2
x = -8, 12
Answer: you wrote it wrong
Step-by-step explanation: