Question

Solve using the quadratic formula x^2-10x+6

Answer 1

`(x-5-√(19))(x-5+√(19))`

Explanation:

1) In general, given
`ax^2+bx+c`, the factored form is:

`a(x-(-b+√(b^2-4ac) )/(2a) )(x-(-b-√(b^2-4ac) )/(2a))`

2) In this case,
`a=1`,
`b= -10` and
`c=6`.

`(x-(10+√((-10)^2-4*6) )/(2) )(x-(10-√((-10)^2-4*6) )/(2) )`

3) Simplify.

`(x-(10+2√(19) )/(2) )(x-(10-2√(19) )/(2) )`

4) Factor out the common term
`2`.

`(x-(2(5+√(19)) )/(2) )(x-(10-2√(19) )/(2) )`

5) Cancel
`2`.

`(x-(5+√(19) ))(x-(10-2√(19) )/(2) )`

6) Remove parentheses.

`(x-5-√(19) )(x-(10-2√(19) )/(2) )`

7) Factor out the common term
`2`.

`(x-5-√(19) )(x-(2(5-√(19)) )/(2) )`

8) Cancel
`2`.

`(x-5-√(19))(x-(5-√(19)))`

9) Remove parentheses.

`(x-5-√(19))(x-5+√(19))`

Thanks,
Eddie Echevarria