The formula for the area of a rectangle is:
A = Length x Height
What we know:
Area = 156
Length = 2x - 1
Height = x + 5
^^^Plug these into the formula given above
156 = (2x - 1) × (x + 5)
156 = (2x - 1)(x + 5)
To solve this let's FOIL (2x - 1) and (x + 5)
FOIL (First, Outside, Inside, Last) like so
First:
(2x - 1)(x + 5) = 156
2x * x
2x²
Outside:
(2x - 1)(x + 5) = 156
2x * 5
10x
Inside:
(2x - 1)(x + 5) = 156
-1 * x
-x
Last:
(2x - 1)(x + 5) = 156
-1 * 5
-5
Now combine all the products of the FOIL together like so...
2x² + 10x + (-x) + (-5) = 156
2x² + 10x - x - 5 = 156
2x² + 9x - 5 = 156
2x² + 9x - 161 = 0
To find what x is you can use the quadratic equation to solve this (quadratic equation in image below)
Remember that quadratic functions are set up like so:
[tex]ax^{2} +bx +c = 0[/tex]
That means that in this equation...
a = 2
b = 9
c = -161
^^^Plug these numbers into the quadratic equation and solve...
[tex]\frac{-9+/-\sqrt{(9)^{2}-4(2)(-161)}}{2(2)}[/tex]
[tex]\frac{-9 +/-\sqrt{81+1288}}{4}[/tex]
[tex]\frac{-9+/-\sqrt{1369}}{4}[/tex]
[tex]\frac{-9+/-37}{4}[/tex]
Keep in mind that +/- is ±
[tex]\frac{-9+37}{4}[/tex] = 7
[tex]\frac{-9-37}{4}[/tex] = -23/2 <<< You can't have a negative length so it will just be 23/2. Also, I believe that you made an error and wrote 23/3 instead of 23/2 :)
Hope this helped!
~Just a girl in love with Shawn Mendes
