Question

Factorize the following algebraic expression:

x2+16x-38=0

please show procedure and tell me which factorization method you used

(NOTE: x2 means x squared)

Answer 1

x^2+16-38=0
find what 2 numbers multiply to get -38 and add to get 16
find factors of 38
2 times 19
there is no way to use common factor so use quadratic formula which is
x=
`( -b+√(b^2-4ac) )/(2a)` or x=
`( -b-√(b^2-4ac) )/(2a)`

ax^2+bx+c=0 subsitte
a=1
b=16
c=-38
subsitute

`( -16+√(16^2-4(1)(-38)) )/(2(1))`=
`( -16+√(256+152) )/(2)`=
`( -16+√(408) )/(2)`=
`( -16+2√(102) )/(2)`=
`-8+√(102)`
so the answers for x are
`-8+√(102)` and
`-8-√(102)` which are aprox -2.099504938362 and +18.099504938362
so it would be
(x-[-8+√102])(x+[8+√102])=0