Question

I need question 8 ( the bonus ) solved for geometry!!

Answer 1

Given:

`(2)/(x-5)=(x-4)/(6)`

Required:

To find the value of x.

Step-by-step explanation:

Consider the given equation,

`(2)/(x-5)=(x-4)/(6)`
`\begin{gathered} (x-5)(x-4)=12 \\ x^2-5x-4x+20=12 \\ x^2-9x+20=12 \\ x^2-9x+8=0 \end{gathered}`

Now, the value of x is

`\begin{gathered} x=(-9\pm√(81-32))/(2) \\ =(-9\pm√(49))/(2) \\ =(-9\pm7)/(2) \end{gathered}`
`\begin{gathered} x=(-9+7)/(2) \\ =(-2)/(2) \\ =-1 \end{gathered}`

OR

`\begin{gathered} x=(-9-7)/(2) \\ =-(16)/(2) \\ =-8 \end{gathered}`

Final Answer:

The values of x are

`x=-1,-8`