minus z both sides
0=x^2+wx+z
we can use quadratic formula or manually complete the square
let's use quadratic
for
0=ax^2+bx+c
[tex]x= \frac{-b+/- \sqrt{b^2-4ac} }{2a} [/tex]
given
0=1x^2+wx-z
a=1
b=w
c=-z
[tex]x= \frac{-w+/- \sqrt{w^2-4(1)(-z)} }{2(1)} [/tex]
[tex]x= \frac{-w+/- \sqrt{w^2+4z} }{2} [/tex]
[tex]x= \frac{-w+ \sqrt{w^2+4z} }{2} [/tex] or [tex]x= \frac{-w- \sqrt{w^2+4z} }{2} [/tex]
