Question

Using the quadratic formula to solve x2+20=2x, what are the values of x​

Answer 1

the answer to the question

Answer 2

`x = 1+ i√(19),1- i√(19)`

Explanation:

Given :
`x^2+20=2x`

To Find: using the quadratic formula find x'

Solution:

Quadratic equation :
`ax^2+bx+c=0` ---1

Quadratic Formula :
`x = (-b\pm√(b^2-4ac))/(2a)`

We are given :
`x^2+20=2x`

`x^2-2x+20=0`

On comparing with 1

a = 1

b = -2

c = 20

Substitute the values in the formula .

`x = (-(-2)\pm√((-2)^2-4(1)(20)))/(2(1))`

`x = (2\pm√(4-80))/(2)`

`x = (2\pm√(-76))/(2)`

`x = (2\pm√(i^2 (2)(2)(19)))/(2)`

`x = (2\pm 2i√(19))/(2)`

`x = 1\pm i√(19)`

`x = 1+ i√(19),1- i√(19)`

Hence The values of x are
`x = 1+ i√(19),1- i√(19)`