Question

In simplest radical form, what are the solutions to the quadratic equation 6=x^2-10x?

Answer 1

`5+2\sqrt{31` and
`5-2\sqrt{31`

Explanation:

First move everything to the same side:

`6=x^2-10x` --->
`x^2-10x-6=0`

Then use the quadratic formula:

x= (-b ±
`√(b^2 -4ac)`)/2a

`a=1\\b=-10 \\c=-6`

x= (-(-10) ±
`√(-10^2 -4*1*-6)`)/2*1

x= (10 ±
`√(100+24)`)/2

Solution 1:

(10 +
`√(1 24)`)/2

`(10+2√(31) )/(2)`=
`5+2\sqrt{31`

Solution 1:

(10 -
`√(1 24)`)/2

`(10-2√(31) )/(2)`=
`5-2\sqrt{31`