Respuesta :

rubahassan583
Answer:
x=(4+5redical(17)) / 4 or
x=(4-5redical(17)) / 4
Step-by-step explanation:
The formula of the area of a rectangle is given by A=L*W
Where L: is the length of the rectangle
And W: is the width of the rectangle
In the above figure, given that:
L=2x-5
W=x
A=50
This forms the equation:
(2x-5)(x)=50
Expand it:
2x^2 - 5x = 50
We are left with the quadratic equation: 2x^2 - 5x - 50 = 0
(a=2, b=-5, c=-50)
To solve a quadratic equation we have to find it's discriminant and check whether it is <0, >0, or =0
Note:
If discriminant<0, the equation has no real root
If discriminant>0, the equation has two real roots in the form of x1=(-b-redical discriminant) / 2a
x2=(-b+redical discriminant) / 2a
If discriminant=0, the equation has one real root in the form of x=-b/2ac
Now, back to our problem:
discriminant= b^2 - 4ac
= (-5)^2 - 4(2)(-50)
= 25 + 400= 425
discriminant=425>0 so the equation has two real roots
x1=(-b-redical discriminant) / 2a
= (-(-4)-redical(425)) / 2(2)
=(4-5redical(17)) / 4
x2=(-b+redical discriminant) / 2a
=(-(-4)+redical(425)) / 2(2)
=(4+5redical(17)) / 4
So as the final answer x=(4+5redical(17)) / 4 or
x=(4-5redical(17)) / 4
HOPE THIS HELPS :)
Hi1315

Answer:

x = 6.40

Step-by-step explanation:

The formula to find the area of the rectangle is :

Area = Length × Width

Given that,

Area ⇒ 50

Length ⇒ ( 2x - 5 )

Width ⇒ x

So now we can write an expression like this.

Area = Length × Width

50  = x ( 2x - 5 )

And now we can solve for x.

Let us solve now by using the completing square method.

x ( 2x - 5 ) = 50

2x² - 5x = 50

First divide the whole equation by 2.

x² - 2.5 = 25

x² - 2.5 + 1.5625 = 25 + 1.5625

( x - 1.25 )² = 26.5625

x - 1.25 = ±√26.5625

x  - 1.25 = ±5.1538

So,

x = + 5.1538 + 1.25                           or        x = - 5.1538 + 1.25

x = 6.40                                                       x = -3.90

As we cannot get a negative number as a value for length,

x = 6.40

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