Answer
{$\frac{5}{3}$}
Work Step by Step
Step 1: Comparing $9x^{2}-30x+25=0$ to the standard form of a quadratic equation, $ax^{2}+bx+c=0$, we find:
$a=9$, $b=-30$ and $c=25$
Step 2: The quadratic formula is:
$x=\frac{-b \pm \sqrt {b^{2}-4ac}}{2a}$
Step 3: Substituting the values of a, b, and c in the formula:
$x=\frac{-(-30) \pm \sqrt {(-30)^{2}-4(9)(25)}}{2(9)}$
Step 4: $x=\frac{30 \pm \sqrt {900-900}}{18}$
Step 5: $x=\frac{30 \pm \sqrt {0}}{18}$
Step 6: $x=\frac{30 \pm 0}{18}$
Step 7: $x=\frac{30}{18}$
Step 8: $x=\frac{5}{3}$
Step 9: Therefore, the solution set is {$\frac{5}{3}$}.
