Question

Eight increase by the square of a number is five times the difference of the number and 2

Answer 1

`x=(5\pm√(47)i)/(2)`

Explanation:

Given : Expression 'eight increase by the square of a number is five times the difference of the number and 2'

To find : Write ans solve the expression ?

Solution :

Let the number be 'x',

Eight increase by the square of a number i.e.
`x^2+8`

Five times the difference of the number and 2 i.e.
`5(x-2)`

Expression is written as

'eight increase by the square of a number is five times the difference of the number and 2'

`x^2+8=5(x-2)`

Solving the expression,

`x^2+8=5x-10`

`x^2-5x+18=0`

Using quadratic formula,
`x=(-b\pm√(b^2-4ac))/(2a)`

Here, a=1 , b=-5 and c=18.

`x=(-(-5)\pm√((-5)^2-4(1)(18)))/(2(1))`

`x=(5\pm√(25-72))/(2)`

`x=(5\pm√(-47))/(2)`

`x=(5\pm√(47)i)/(2)`