SOLUTION: I am having trouble telling if the equation has one, two, or no solutions: {{{x^2-15x+56=0}}}

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Question 774694: I am having trouble telling if the equation has one, two, or no solutions: x%5E2-15x%2B56=0
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2-15x%2B56=0....first factor completely so we can use zero product rule; write -15x as -7x-8x
x%5E2-7x-8x%2B56+=+0......group
%28x%5E2-7x%29-%288x-56+%29=+0...factor
x%28x-7%29-8%28x-7+%29=+0
%28x-8%29%28x-7%29+=+0
solutions:
if %28x-8%29+=+0, then x=8
if %28x-7%29+=+0, then x=7
so, you have two real solutions
let's see them on a graph
+graph%28+600%2C+600%2C+-2%2C+15%2C+-2%2C+10%2C+x%5E2-15x%2B56%29+