Question

How do you solve `x^2+8=0` using the quadratic formula?

Answer 1

`x=2sqrt(2)color(white)("x")icolor(white)("XXX")orcolor(white)("XXX")x=-2sqrt(2)color(white)("x")i`

(see below for use of the quadratic formula)

Explanation:

Standard quadratic form for an equation is:
`color(white)("XXX")color(red)ax^2+color(blue)bx+color(magenta)c=0`
and in this form the solutions are given by
`color(white)("XXX")x=(-color(blue)b+-sqrt(color(blue)b^2-4color(red)acolor(magenta)c))/(2color(red)a)`

Expressing the given equation into standard form:
`x^2+8=0`
`color(white)("XXX")rarr color(red)1x^2+color(blue)0 * x +color(magenta)8 = 0`
with solutions:
`color(white)("XXX")x=(-color(blue)0+-sqrt(color(blue)0^2-4 * color(red)1 * color(magenta)8))/(2 * color(red)1)`

`color(white)("XXX")=+-sqrt(-32)/2=+-(4sqrt(2)color(white)("x")i)/2=+-2sqrt(2)color(white)("x")i`