Question 115691
To find the x-intercepts, set the right side equal to zero



{{{-x^2+15x-56=0}}}



{{{-(x^2-15x+56)=0}}} Factor out a -1



{{{-(x-8)(x-7)=0}}} Factor the left side (note: if you need help with factoring, check out this <a href=http://www.algebra.com/algebra/homework/playground/change-this-name4450.solver>solver</a>)




Now set each factor equal to zero:

{{{x-8=0}}} or  {{{x-7=0}}} 


{{{x=8}}} or  {{{x=7}}}    Now solve for x in each case



So our answer is 

 {{{x=8}}} or  {{{x=7}}} 



Notice if we graph {{{y=-x^2+15x-56}}} we can see that the roots are {{{x=8}}} and  {{{x=7}}} . So this visually verifies our answer.



{{{ graph(500,500,-10,10,-10,10,0, -x^2+15x-56) }}}