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A garden has dimensions 2x+3 ft by x+6 ft. If the garden is 95 ft^2, then what are the dimensions. Solve by factoring

 Apr 8, 2020
 #1
avatar+9477 
+2

A garden has dimensions 2x+3 ft by x+6 ft. If the garden is 95 ft^2, then what are the dimensions. Solve by factoring.

 

Hello Guest!

 

\((2x+3)\cdot (x+6)=95\\ 2x^2+12x+3x+18-95=0\\ 2x^2+15x-77=0\)

\(x = {-b \pm \sqrt{b^2-4ac} \over 2a}\)

\(x = {-15 \pm \sqrt{15^2+4\cdot 2\cdot 77} \over 2\cdot 2}\\ x=\frac{-15\pm 29}{4}\)

\(x_1=3.5\\ x_2\ not\ applicable\)

 

The dimensiones are \(10ft\times 9.5ft\)

laugh  !

 Apr 9, 2020
 #2
avatar+111329 
+1

(2x + 3) ( x + 6)  =  95

 

2x^2 + 3x  + 12x + 18  =  95    simpify

 

2x^2  + 15x  - 77  =  0      factor as

 

(2x  - 7) ( x + 11)  =   0

 

Only   the first  factor set to  0  produces  what we want

 

2x  - 7  =   0

 

2x   =  7

 

x  = 7/2 

 

One  dimension =  (2(7/2) + 3)  =  ( 7 + 3)  =  10 ft

 

The  other  is  95  /10   = 9.5 ft

 

 

cool cool cool

 Apr 9, 2020

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