Question

What is the solution of sqrt x^2 + 49 = x +5

Answer 1

The first option. x=12/5

Answer 2

Given equation: $\sqrt{x^2\:+\:49}=x+5.$

$\mathrm{Square\:both\:sides}$

$\left(\sqrt{x^2+49}\right)^2=\left(x+5\right)^2$

$\mathrm{Expand\:}\left(\sqrt{x^2+49}\right)^2:\quad x^2+49$

$\mathrm{Expand\:}\left(x+5\right)^2:\quad x^2+10x+25$

$x^2+49=x^2+10x+25$

$\mathrm{Subtract\:}x^2\mathrm{\:from\:both\:sides}$

$x^2+49-x^2=x^2+10x+25-x^2$

$49=10x+25$

$10x+25=49$

$\mathrm{Subtract\:}25\mathrm{\:from\:both\:sides}$

$10x+25-25=49-25$

$10x=24$

$\mathrm{Divide\:both\:sides\:by\:}10$

$\frac{10x}{10}=\frac{24}{10}$

$x=\frac{12}{5}$

Therefore, correct option is first option $x=\frac{12}{5}.$