Question

solve the following equation for x: z=x^2+wx

Answer 1

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
$x= \frac{-b+/- \sqrt{b^2-4ac} }{2a}$
given
0=1x^2+wx-z
a=1
b=w
c=-z

$x= \frac{-w+/- \sqrt{w^2-4(1)(-z)} }{2(1)}$
$x= \frac{-w+/- \sqrt{w^2+4z} }{2}$

$x= \frac{-w+ \sqrt{w^2+4z} }{2}$ or $x= \frac{-w- \sqrt{w^2+4z} }{2}$