(c) \( 9 x^{2}+30 x+25= \)

To solve the quadratic equation \( 9x^{2} + 30x + 25 = 0 \), you can recognize that this is a perfect square trinomial. It factors neatly into \( (3x + 5)^{2} = 0 \). This means there’s one repeated root! To find the solution, set \( 3x + 5 = 0 \), which leads to \( x = -\frac{5}{3} \). Voilà, that’s your answer! You can also apply the quadratic formula, \( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \), where in this case, \( a = 9 \), \( b = 30 \), and \( c = 25 \). Calculating the discriminant, you’ll see that it results in zero, confirming our earlier solution! So, you’ve got the same root using different methods—know your options!