please help to find value of x?

Question

you want to build a shed in your backyard. you have blueprints which show that the shed is10 feet x 13 feet. you want to change the dimensions. the new area is modeld by the equation A = -xSquared + 3x + 130.
What value of x, if any, will give an area of 140 ftSquared? Is there any value of x for which the shed has an area of 124 ftSquared? If so, what value of x?

Answer 1

Ok, let' see...

The equation for the Area = - x^2 + 3x + 130

if Area = 140 sqft

140 = - x^2 + 3x + 130

Rearranging terms,

x^2 - 3x +10 = 0

compleating the square,

(x-1.5)(x-1.5) + 10 - 2.25 = 0

we can see trouble here because the final equation
looks like,

(x-1.5)^2 = -7.75 which will provide a negative square root value.

So, no real x will satify the above equation for A = 140.

For A = 124 we follow the same procedure as described previoulsy,

124 = -x^2 + 3x + 130

x^2 - 3x - 6 = 0

(x-1.5)(x-1.5) - 6 - 2.25 = 0

(x-1.5)^2 = 8.25

taking square root of both sides of the equation,

x-1.5 = +/- sqrt(8.25)

x = 1.5 +/- sqrt(8.25)

x= 1.5 +/- 2.87

x= 4.37
x= -1.37 so pick x = 4.37

Hope this helps!

Answer 2

A = -xSquared + 3x + 130. when the A is 140 ftsquared, the answer is 2, if you use a method called completing the square. there is no integer if it is 124ft squared.

Answer 3

140 = -x^2 + 3x + 130
-x^2 + 3x - 10 = 0
x^2 - 3x + 10 = 0
(x - 5)(x + 2) = 0
x = 5 or -2

Since you can't have negative length

x = 5

ANS : x = 5ft

-----------------------------------------

124 = -x^2 + 3x + 130
-x^2 + 3x + 6 = 0
x^2 - 3x - 6 = 0

x = (-b ± sqrt(b^2 - 4ac))/(2a)

x = (-(-3) ± sqrt((-3)^2 - 4(1)(-6)))/(2(1))
x = (3 ± sqrt(9 + 24))/2
x = (3 ± sqrt(33))/2

x = (1/2)(3 ± sqrt(33))

Can't have a negative length

x = (1/2)(3 + sqrt(33))
x = about 4.37228 or about 4.4 ft

ANS : about 4.4 ft

Answer 4

The answer is 4.

Answer 5

confusing question. x=2 maybe unless a trick question