simplify 2r^2-28r+38=0

Hi TitaniumRome, 

You have to give explanations - they can probably get the answer only from the back of the book.

Your role as an answerer is to help people learn :)

did it, heres your answer:

{r=7-sqrt(30), r=sqrt(30)+7}

2r² - 28r + 38  =  0

Divide all the terms by 2:

r² - 14r + 19  =  0

Since this can't be factored easily, if you use the quadratic formula:

a = 1     b = -14     c = 19

r  =  [-b ± √(b² - 4·a·c)]/(2·a)   --->   r  =  [- -14 ± √( (-14)² - 4·1·19)]/(2·1)

--->   r  =  [14 ± √( 196 - 76)]/(2)    --->   r  =  [14 ± √(120)]/(2)   --->   r  =  [14 ± √4√(30)]/(2)

--->   r  =  [14 ± 2√(30)]/(2)   --->   r  =  7 ± √(30)