Question

solve for u.
$9u^2 - 30u + 25 = 0$
write each solution as an integer, proper fraction, or improper fraction in simplest form. if there are multiple solutions, separate them with commas.
$u = $

Explanation:

Step1: Recognize the quadratic form

The equation \(9u^2 - 30u + 25 = 0\) is a quadratic equation. Notice that it might be a perfect square trinomial. Recall that \((a - b)^2=a^2 - 2ab + b^2\).
For \(9u^2=(3u)^2\), \(25 = 5^2\), and \(- 30u=-2\times(3u)\times5\). So the left - hand side can be factored as a perfect square.
\(9u^2 - 30u + 25=(3u - 5)^2\)
So the equation becomes \((3u - 5)^2=0\)

Step2: Solve for u

Set \(3u - 5 = 0\) (since a square of a number is zero only when the number itself is zero).
Add 5 to both sides: \(3u=5\)
Divide both sides by 3: \(u=\frac{5}{3}\) (and since this is a repeated root, there's only one distinct solution)

Answer:

\(\frac{5}{3}\)