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Solve for $u$ . $\newline$ $9u^2 - 30u + 25 = 0$ $\newline$ Write each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas. $\newline$ $u = \_\_\_$

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Solve polynomial equations

Full solution

Q. Solve for

u

.

\newline

9u^2 - 30u + 25 = 0

\newline

Write each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas.

\newline

u = \_\_\_

Factor the quadratic: First, let's see if the quadratic can be factored easily. We're looking for two numbers that multiply to $9\times25$ (which is $225$ ) and add up to $-30$ .
Identify correct numbers: The numbers that work are $-15$ and $-15$ because $-15 \times -15 = 225$ and $-15 + -15 = -30$ .
Write the quadratic: Now we can write the quadratic as $(3u - 5)(3u - 5) = 0$ .
Set factors equal to zero: Set each factor equal to zero: $3u - 5 = 0$ .
Solve for u: Solve for u: $3u = 5$ , so $u = \frac{5}{3}$ .
Final solution: Since both factors were the same, there's only one solution: $u = \frac{5}{3}$ .

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