Given equation: [tex]\sqrt{x^2\:+\:49}=x+5.[/tex]
[tex]\mathrm{Square\:both\:sides}[/tex]
[tex]\left(\sqrt{x^2+49}\right)^2=\left(x+5\right)^2[/tex]
[tex]\mathrm{Expand\:}\left(\sqrt{x^2+49}\right)^2:\quad x^2+49[/tex]
[tex]\mathrm{Expand\:}\left(x+5\right)^2:\quad x^2+10x+25[/tex]
[tex]x^2+49=x^2+10x+25[/tex]
[tex]\mathrm{Subtract\:}x^2\mathrm{\:from\:both\:sides}[/tex]
[tex]x^2+49-x^2=x^2+10x+25-x^2[/tex]
[tex]49=10x+25[/tex]
[tex]10x+25=49[/tex]
[tex]\mathrm{Subtract\:}25\mathrm{\:from\:both\:sides}[/tex]
[tex]10x+25-25=49-25[/tex]
[tex]10x=24[/tex]
[tex]\mathrm{Divide\:both\:sides\:by\:}10[/tex]
[tex]\frac{10x}{10}=\frac{24}{10}[/tex]
[tex]x=\frac{12}{5}[/tex]
Therefore, correct option is first option [tex]x=\frac{12}{5}.[/tex]
