Question 1010099

 {{{sqrt(8x+49)-sqrt(2x+28)=3 }}}

 {{{(sqrt(8x+49)-sqrt(2x+28))^2=3^2 }}}

 {{{(sqrt(8x+49))^2-2sqrt(8x+49)*sqrt(2x+28)+(sqrt(2x+28))^2=9 }}}

{{{8x+49-2sqrt((2x+28)(8x+49))+2x+28=9 }}}

{{{10x+77-2sqrt((2x+28)(8x+49))=9 }}}

{{{10x+77-9=2sqrt((2x+28)(8x+49)) }}}

{{{10x+68=2sqrt((2x+28)(8x+49)) }}}

{{{(10x+68)^2=(2sqrt((2x+28)(8x+49)))^2 }}}

{{{100x^2+1360x+4624=4(16x^2+322x+1372) }}}

{{{100x^2+1360x+4624=64x^2+1288x+5488 }}}

{{{100x^2+1360x+4624-64x^2-1288x-5488=0 }}}

{{{(100x^2-64x^2)+(1360x-1288x)+(4624-5488)=0 }}}

{{{36x^2+72x-864=0 }}}

{{{36x^2/36+72x/36-864/36=0 }}}

{{{x^2+2x-24=0 }}}

{{{x^2+6x-4x-24=0 }}}

{{{(x^2+6x)-(4x+24)=0 }}}

{{{x(x+6)-4(x+6)=0 }}}

{{{(x-4)(x+6) = 0}}}

solutions:

{{{x=4}}}
{{{x=-6}}}

since {{{x=-6}}} will make in {{{sqrt(8x+49)}}} negative radicand which will give us complex zero, we will take only  {{{highlight(x=4)}}} as a solution