Question 960522

{{{sqrt(x-14) + sqrt(x-5) = 3}}}........square both sides


{{{(sqrt(x-14) + sqrt(x-5))^2 = 3^2}}}


{{{(sqrt(x-14))^2+2sqrt(x-14)*sqrt(x-5) + sqrt(x-5)^2 = 9}}}


{{{x-14+2sqrt((x-14)(x-5)) + x-5 = 9}}}


{{{2x-19+2sqrt((x-14)(x-5))  = 9}}}


{{{2sqrt((x-14)(x-5))  = 9+19-2x}}}


{{{2sqrt((x-14)(x-5))  = 28-2x}}}.........simplify


{{{2sqrt((x-14)(x-5))/2  = 28/2-2x/2}}}


{{{sqrt((x-14)(x-5))  = 14-x}}} .......square both sides again


{{{(sqrt((x-14)(x-5)))^2  = (14-x)^2}}} 


{{{(x-14)(x-5)  = 14^2-28x+x^2}}} 


{{{cross(x^2)-5x-14x+70  = 196-28x+cross(x^2)}}}


{{{-19x+70  = 196-28x}}}


{{{-19x+28x  = 196-70}}}  


{{{9x  = 126}}} 


{{{x  = 126/9}}}


{{{x  = 14}}}