Question 3010
domain is basically all the valid numbers you can put into an equation without it breaking...the x-values


range is that set of number you get out of the equation if you put all the values of the domain into it...the y-values.


{{{(-40 +- sqrt(-1472))/32}}}
{{{(-40 +- sqrt(1472*(-1)))/32}}}
{{{(-40 +- sqrt(1472)sqrt(-1))/32}}}
{{{(-40 +- sqrt(1472)i)/32}}}


Now to simplify the 1472...2*736....4*368... 16*92... 64*23...we have a square root, so look for a number that will have a nice root, like 4, 9, 16, 25, 36, 49, 64 etc


so {{{sqrt(1472)}}} can be written as {{{sqrt(64*23)}}} which is {{{sqrt(64)sqrt(23)}}} which is {{{8sqrt(23)}}}


So, our calculation now becomes: {{{(-40 +- 8sqrt(23)i)/32}}} which is what you said, and this can simplify a little further to {{{(-8(5 +- sqrt(23)i))/32}}} which is {{{(-5 +- sqrt(23)i)/4}}}

jon