Answer
{$0,\frac{5}{2}$}
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: $3(4x-5)^{2}-50=25$
Step 2: $3(4x-5)^{2}=25+50$
Step 3: $3(4x-5)^{2}=75$
Step 4: $(4x-5)^{2}=25$
Step 5: $4x-5=\pm \sqrt {25}$
Step 6: $4x-5=\pm 5$
Step 7: $4x-5=5$ or $4x-5=-5$
Step 8: $4x=5+5$ or $4x=-5+5$
Step 9: $4x=10$ or $4x=0$
Step 10: $x=\frac{10}{4}$ or $x=\frac{0}{4}$
Step 11: $x=\frac{5}{2}$ or $x=0$
The solution set is {$0,\frac{5}{2}$}.
