Answer:
![x^2+ 18x -130=0](https://tex.z-dn.net/?f=x%5E2%2B%2018x%20-130%3D0)
Step-by-step explanation:
Given
See attachment for diagram
Required
The equation to find x
First, calculate the area of the big rectangle using:
![Area = Length * Width](https://tex.z-dn.net/?f=Area%20%3D%20Length%20%2A%20Width)
So:
![A_1 = (x + 6) * (3x - 2)](https://tex.z-dn.net/?f=A_1%20%3D%20%28x%20%2B%206%29%20%2A%20%283x%20-%202%29)
The smaller rectangle
![A_2 = (x - 1) * (2x)](https://tex.z-dn.net/?f=A_2%20%3D%20%28x%20-%201%29%20%2A%20%282x%29)
The difference between this areas give the area of the shaded region.
So:
![A_1 - A_1 = 118](https://tex.z-dn.net/?f=A_1%20-%20A_1%20%3D%20118)
![(x+6)*(3x-2) - (x-1)*2x = 118](https://tex.z-dn.net/?f=%28x%2B6%29%2A%283x-2%29%20-%20%28x-1%29%2A2x%20%3D%20118)
Open brackets
![3x^2 - 2x + 18x -12 -2x^2 +2x = 118](https://tex.z-dn.net/?f=3x%5E2%20-%202x%20%2B%2018x%20-12%20-2x%5E2%20%2B2x%20%3D%20118)
Collect like terms
![3x^2 -2x^2- 2x +2x+ 18x -12 - 118=0](https://tex.z-dn.net/?f=3x%5E2%20-2x%5E2-%202x%20%2B2x%2B%2018x%20-12%20%20%20-%20118%3D0)
![x^2+ 18x -130=0](https://tex.z-dn.net/?f=x%5E2%2B%2018x%20-130%3D0)
<em>The above equation can be used to solve for x</em>
The answer is 80 because you add then subtract
1) 0.78
2) 34.28
This is because the number in the 3rd decimal place for both numbers is 5 or above so it is rounded up rather than down.