Question

Guided Practice

The length of the model is 2x + 1 and the width is x + 1. If the total area is 28 square units, write an equation to find x. Then solve for x by completing the square.


A.
2x2 + 3x + 1 = 28; x = 3


B.
2x2 + 3x +1 = 28; x = −184


C.
2x2 = 28; x = 14⎯⎯⎯⎯√

Answer 1

The actual answer is A. 2x^2 + 3x + 1 = 28; x = 3

Explanation:

First, we get the information:

L=2x+1 W=x+1 A=28

We then get the area formula.

L * W = A

So after that, we plug the equations above into the formula, and we get this.

(2x+1) * (x+1) = 28

Solve for it.

2x+1

* x+1

2x+1

2x^2 +x

2x^2+3x+1

2x^2+3x+1=28 <--- solve now! : )

2 x^ 2 + 3 x + 1 − 2 8 = 0

2 x ^2 + 3 x − 2 7 = 0

2 x ^2 + 9 x − 6 x − 2 7 = 0 (For here, you have to add another thing)

( 2 x ^2 + 9 x ) + ( − 6 x − 2 7 ) = 0 (now do common factor, which is group them)

x( 2 x + 9 ) − 3 ( 2 x + 9 ) = 0

(2x+9)(x-3)=0 now, you have to separate the equation into two.

x-3=0 2x+9=0

x=3 x=-9/2

So, one of them is 3, just as choice A.

Answer 2

The length of the model = 2x+1

The width of the model = x+1

The total surface area given = 28 unit²

so the equation forms

(x+1)(2x+1) = 28unit²

x(2x+1)+1(2x+1) = 28unit²

2x²+x+2x+1 =28 unit²

2x²+3x+1 = 28 unit²

2x²+3x = 27 unit²

2x²+3x-27 = 0

now the equation is in the form of ax²+bx+c = 0

so if a = 2 ,b = 3 and c = -27

then we know ax²+bx+c= 0

so x = -b±√b²-4ac/2a

so here x = -3±√9+216/4

x= -3±√255/4

so x₁ = -3+√255/4 = 3.24 units

and x₂ = -3-√255/4 = -4.74 units

so x{3.24,-4.74}units (ans)

Hope it helps