SOLUTION: Solve If f(x)={{{sqrt(2x-3)}}} and g(x)={{{sqrt(x+7)}}}-2,find any x for which f(x)=g(x)

Algebra ->  Radicals -> SOLUTION: Solve If f(x)={{{sqrt(2x-3)}}} and g(x)={{{sqrt(x+7)}}}-2,find any x for which f(x)=g(x)      Log On


   

Question 742835: Solve
If f(x)=sqrt%282x-3%29 and g(x)=sqrt%28x%2B7%29-2,find any x for which f(x)=g(x)
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29=sqrt%282x-3%29 and g%28x%29=sqrt%28x%2B7%29-2
f%28x%29=g%28x%29 for:
sqrt%282x-3%29=sqrt%28x%2B7%29-2
%28sqrt%282x-3%29%29%5E2=%28sqrt%28x%2B7%29-2%29%5E2
2x-3=%28sqrt%28x%2B7%29%29%5E2-2%28-2%29%28sqrt%28x%2B7%29%29%2B%28-2%29%5E2
2x-3=x%2B7%2B4%28sqrt%28x%2B7%29%29%2B4
2x-x-7-4-3=4sqrt%28x%2B7%29
x-14=4sqrt%28x%2B7%29
%28x-14%29%5E2=%284sqrt%28x%2B7%29%29%5E2
x%5E2-28x%2B196=16%28x%2B7%29
x%5E2-28x%2B196=16x%2B112
x%5E2-28x%2B196-16x-112=0
x%5E2-44x%2B84=0.......write -44x as -2x-42x
x%5E2-2x-42x%2B84=0 ...group
%28x%5E2-2x%29-%2842x-84%29=0
x%28x-2%29-42%28x-2%29=0
%28x-42%29%28x-2%29=0

solutions:
if
%28x-42%29=0 => x=42

if
%28x-2%29=0 => x=2