Question

Factorize the following algebraic expression:

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=$\frac{ -b+\sqrt{b^2-4ac} }{2a}$ or x=$\frac{ -b-\sqrt{b^2-4ac} }{2a}$

ax^2+bx+c=0 subsitte
a=1
b=16
c=-38
subsitute
$\frac{ -16+\sqrt{16^2-4(1)(-38)} }{2(1)}$=$\frac{ -16+\sqrt{256+152} }{2}$= $\frac{ -16+\sqrt{408} }{2}$= $\frac{ -16+2\sqrt{102} }{2}$=$-8+\sqrt{102}$
so the answers for x are $-8+\sqrt{102}$ and $-8-\sqrt{102}$  which are aprox -2.099504938362 and +18.099504938362
so it would be
(x-[-8+√102])(x+[8+√102])=0