Question

FACTOR:

2x^2-17x-33

and find the extraneous soultion, if there is any.

ALL WORK SHOWN (or at least most of it)
thank you!!!

Answer 1

`2x^2-17x-33 : \text{Factor}`


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


`2(x- (17+ √((-17)^2)-4*2*-33 )/(2*2), x-(17- √((-17)^2)-4*2*-33 )/(2*2)`


`2(x- (17+ √(553) )/( 4), x- (17- √(553) )/( 4))`

Answer 2

2x^2-17x-33=0 let's complete the square, add 33 to both sides

2x^2-17x=33 make the leading coefficient equal to one, divide all by 2

x^2-8.5=16.5 halve the linear coefficient, square it, and add that to both sides

x^2-8.5+18.0625=34.5625 now left side is a perfect square

(x-4.25)^2=34.5625 take the square root of both sides

x-4.25=±√34.5625 add 4.25 to both sides

x=4.25±√34.5625 so the factors are:

(x+4.25+√34.5625)(x+4.25-√34.5625)