Answer:
[tex]x^2+ 18x -130=0[/tex]
Step-by-step explanation:
Given
See attachment for diagram
Required
The equation to find x
First, calculate the area of the big rectangle using:
[tex]Area = Length * Width[/tex]
So:
[tex]A_1 = (x + 6) * (3x - 2)[/tex]
The smaller rectangle
[tex]A_2 = (x - 1) * (2x)[/tex]
The difference between this areas give the area of the shaded region.
So:
[tex]A_1 - A_1 = 118[/tex]
[tex](x+6)*(3x-2) - (x-1)*2x = 118[/tex]
Open brackets
[tex]3x^2 - 2x + 18x -12 -2x^2 +2x = 118[/tex]
Collect like terms
[tex]3x^2 -2x^2- 2x +2x+ 18x -12 - 118=0[/tex]
[tex]x^2+ 18x -130=0[/tex]
The above equation can be used to solve for x
