Question 318144
The midpoint of the points (a,b) and (c,d) is (p,q) where {{{p=(a+c)/2}}} and {{{q=(b+d)/2}}}. In this case, {{{a=6}}}, {{{b=-1}}}, {{{p=15/2}}} and {{{q=2}}}. Plug these values in to get:


{{{15/2=(6+c)/2}}} and {{{2=(-1+d)/2}}}


I'll let you solve those equations.


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From {{{v^2-7v+5}}} we can see that {{{a=1}}}, {{{b=-7}}}, and {{{c=5}}}



{{{D=b^2-4ac}}} Start with the discriminant formula.



{{{D=(-7)^2-4(1)(5)}}} Plug in {{{a=1}}}, {{{b=-7}}}, and {{{c=5}}}



{{{D=49-4(1)(5)}}} Square {{{-7}}} to get {{{49}}}



{{{D=49-20}}} Multiply {{{4(1)(5)}}} to get {{{(4)(5)=20}}}



{{{D=29}}} Subtract {{{20}}} from {{{49}}} to get {{{29}}}



Since the discriminant is greater than zero, this means that there are two real solutions.