Question 845911
The only mistake is the incorrect case-level for x.  Otherwise, your steps are good.  What is stopping your from continuing?


Is {{{x^2+13x-285}}} factorable?  If you believe so, then find the factorization.  If you are not sure if factorable, use the general solution of a quadratic equation.


{{{285=3*5*19}}}.  A value of 13 will not come from any of this.


General Solution:
{{{D=13^2-4(-285)=169+1140=1309}}}
Also {{{D=1309=7*11*17}}}, three prime factors.
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{{{x=(-13+sqrt(D))/2}}}
{{{highlight(x=(-13+sqrt(1309))/2)}}}