Question 742835
{{{f(x)=sqrt(2x-3)}}} and {{{g(x)=sqrt(x+7)-2}}}

{{{f(x)=g(x)}}} for:

{{{sqrt(2x-3)=sqrt(x+7)-2}}}

{{{(sqrt(2x-3))^2=(sqrt(x+7)-2)^2}}}

{{{2x-3=(sqrt(x+7))^2-2(-2)(sqrt(x+7))+(-2)^2}}}

{{{2x-3=x+7+4(sqrt(x+7))+4}}}

{{{2x-x-7-4-3=4sqrt(x+7)}}}

{{{x-14=4sqrt(x+7)}}}

{{{(x-14)^2=(4sqrt(x+7))^2}}}

{{{x^2-28x+196=16(x+7)}}}

{{{x^2-28x+196=16x+112}}}

{{{x^2-28x+196-16x-112=0}}}

{{{x^2-44x+84=0}}}.......write {{{-44x}}} as  {{{-2x-42x}}}

{{{x^2-2x-42x+84=0}}} ...group

{{{(x^2-2x)-(42x-84)=0}}}

{{{x(x-2)-42(x-2)=0}}}

{{{(x-42)(x-2)=0}}}  


solutions:

if 
{{{(x-42)=0}}} => {{{x=42}}}
      
if 
{{{(x-2)=0}}} => {{{x=2}}}


{{{drawing(600, 600, -10,45, -10, 10,circle(2,1,0.3),circle(42,-9,0.3), graph( 600, 600, -10,45, -10, 10, sqrt(2x-3),sqrt(x+7)-2,-sqrt(2x-3),-sqrt(x+7)-2)) }}}