Answer
{$\frac{5- 2\sqrt {10}}{3},\frac{5+ 2\sqrt {10}}{3}$}
Work Step by Step
Using Property 10.1, which states that for any non-negative real number $a$, $x^{2}=a$ can be written as $x=\pm\sqrt a$, we obtain:
Step 1: $(3x-5)^{2}=40$
Step 2: $3x-5=\pm \sqrt {40}$
Step 3: $3x-5=\pm \sqrt {4\times10}$
Step 4: $3x-5=\pm \sqrt {2^{2}\times10}$
Step 5: $3x-5=\pm 2\sqrt {10}$
Step 6: $3x-5=+ 2\sqrt {10}$ or $3x-5=-2 \sqrt {10}$
Step 7: $3x=5+ 2\sqrt {10}$ or $3x=5-2 \sqrt {10}$
Step 8: $x=\frac{5+ 2\sqrt {10}}{3}$ or $x=\frac{5- 2\sqrt {10}}{3}$
The solution set is {$\frac{5- 2\sqrt {10}}{3},\frac{5+ 2\sqrt {10}}{3}$}.
